Use the slope formula to identify the rise and the run. What is the required slope? a fraction, like 7 / 4 7/4 7/4. or you could look at it as your run being negative so you go left. Can someone explain it to me? Use the slope formula [latex]m=\Large\frac{\text{rise}}{\text{run}}[/latex] to identify the rise and the run. Convert [latex]1[/latex] foot to [latex]12[/latex] inches. [latex]m={\Large\frac{-\frac{1}{4}\text{in}\text{.}}{12\text{in. Khan Academy is a 501(c)(3) nonprofit organization. We count [latex]3[/latex] units up and [latex]4[/latex] units right. Graph [latex]y=\frac{1}{2}x-4[/latex] using the slope-intercept equation. Ex: Graph a Line Given a Point and the Slope. Have you ever thought about the sewage pipes going from your house to the street? where $A, B,$ and $C$ [latex] \displaystyle y=\frac{1}{2}x-5[/latex]. Direct link to Kim Seidel's post Put a point at (0, -1/2)., Posted a month ago. It will help you to find the coefficients of slope and y-intercept, as well as the x-intercept, using the slope intercept formulas. Quiz 1: 5 questions Practice what you've learned, and level up on the above skills. In the following video we show another example of how to graph a line given a point on the line and the slope of the line. [latex]m={\Large\frac{-\frac{1}{4}\text{in}\text{.}}{12\text{in. Their slope is an important factor in how they take waste away from your house. Graph the line passing through the point [latex]\left(1,-1\right)[/latex] whose slope is [latex]m=\Large\frac{3}{4}[/latex]. We can plot the point by starting at the origin and counting down 4 to get to (0,-4) and put a dot at this point. Direct link to David Severin's post If you have an equation i, Posted 3 years ago. Then we connect the points with a line and draw arrows at the ends to show it continues. Worked example: solutions to 2-variable equations, Completing solutions to 2-variable equations, Complete solutions to 2-variable equations, Level up on the above skills and collect up to 400 Mastery points, Level up on the above skills and collect up to 240 Mastery points, Graphing lines from slope-intercept form review, Slope-intercept equation from slope & point, Intro to graphing two-variable inequalities. Solution Plot the given point, [latex]\left(1,-1\right)[/latex]. To go from one to five, we added four. Plot the given point, the [latex]y[/latex] -intercept [latex]\left(0,2\right)[/latex]. The pitch of a buildings roof is the slope of the roof. Trying to graph a line from a given slope and a point? Alright, so remember, slope Given two points, it is possible to find using the following equation: Given the points (3,4) and (6,8) find the slope of the line, the distance between the two points, and the angle of incline: While this is beyond the scope of this calculator, aside from its basic linear use, the concept of a slope is important in differential calculus. . Connect the points with a line. And I got the signs right, So the point slope equation for coordinates \ (\left (-6,8\right)\) , and slope 5 will be \ (5x - y + 38.\) Let's calculate the point slope form by using given values. Direct link to 2024oshiroc's post brah can sum1 help me I n, Posted 2 months ago. CC licensed content, Specific attribution, [latex]\Large\frac{\text{rise}}{\text{run}}\normalsize=\Large\frac{4}{1}[/latex], [latex]\text{rise}=4\text{ run}=1[/latex], Draw the graph of a line using slope and a point on the line, Write the equation of a line using slope and y-intercept. Graph a line given a point and a slope Plot the given point. If you're seeing this message, it means we're having trouble loading external resources on our website. Posted 4 years ago. Our change in y is our finishing y one minus our starting y four, which First, plot the [latex]y[/latex]-intercept. y. At the beginning of this section, we said there are many applications of slope in the real world. In this tutorial, you'll see how to identify the x-coordinate in an ordered pair! With a slope of rise (up) 3 over run (right) 1, you get to (0+1,-4+3) which is (1,-1), and a second time (1+1,-1+3) which is (2,2) and you have three points to draw a line through. What is the slope of the roof shown? Write the equation of the line that has a slope of [latex] \displaystyle \frac{1}{2}[/latex] and a y-intercept of [latex]5[/latex]. Algebra 1 > Forms of linear equations > Intro to slope-intercept form Cookie Notice Intro to slope-intercept form Google Classroom About Transcript Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line. Or, use <Shift> with a mouse to zoom and move. Solution Graph a line given a point and the slope. Well, it's going to be, our change in y is negative three and our change in x is one. Solutions to two-variable linear equations. When x increases, y increased as well. Direct link to I am Rilakkuma(TheCool)'s post HURRAY, LOCKDOWN IS OVER!, Posted 3 years ago. When this happens, we use the definition of slope to draw the graph of the line. That all depends on what your choice of careers is. Refer to the Triangle Calculator for more detail on the Pythagorean theorem as well as how to calculate the angle of incline provided in the calculator above. [latex]\begin{array}{}\\ \\ m=-\frac{2}{3}\hfill \\ \frac{\text{rise}}{\text{run}}=\frac{-2}{3}\hfill \\ \\ \\ \text{rise}=-2\hfill \\ \text{run}=3\hfill \end{array}[/latex]. Use the slope formula to identify the rise and the run. The x- and y-axes each scale by one. You can use slope formula to calculate it. Learn how to graph lines whose equations are given in the slope-intercept form y=mx+b. Use the slope formula m = rise run to identify the rise and the run. We will give some examples here and then we will show below why this case is so important. use graphs. Identify one other point and draw a slope triangle to find the slope. A coordinate plane. If you're seeing this message, it means we're having trouble loading external resources on our website. . It can also be seen that x and y are line segments that form a right triangle with hypotenuse d, with d being the distance between the points (x1, y1) and (x2, y2). Direct link to bail380001's post what if the question is y, Posted a month ago. who else is watching in quarantine for online school classes? Direct link to FrozenFern's post How do I graph a line if , Posted 2 years ago. Google Classroom. We also learned how to graph lines by plotting points, by using intercepts, and by recognizing horizontal and vertical lines. As before, we can tell that the line passes through the, We need a way to find another point on the line whose coordinates are integers. The slope would then be -1/3, when you get negitive and negitive. The slope intercept form calculator will teach you how to find the equation of a line from any two points that this line passes through. Im using the first example here to demonstrate. So what's our change in x? When we have an equation in slope-intercept form we can graph it by first plottingthe y-intercept, then using the slope, find a second point and connecting the dots. [latex]\begin{array}{}\\ \\ m=-\frac{2}{3}\hfill \\ \frac{\text{rise}}{\text{run}}=\frac{-2}{3}\hfill \\ \\ \\ \text{rise}=-2\hfill \\ \text{run}=3\hfill \end{array}[/latex]. Ex: y=2x-1/2. rise. Starting at the given point, count out the rise and run to mark the second point. Algebra Slope and Y-Intercept Calculator Step 1: Enter the linear equation you want to find the slope and y-intercept for into the editor. If you start with s slope of 1, it is at a 45 degree angle where y=x. We will now show you what is so special about the case in which the given point is the y-intercept. A slope of two requires you to go up 2 (y change) /1 (x change). Plot the given point, [latex]\left(1,-1\right)[/latex]. three divided by one is negative three. Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! Direct link to 20nlion's post im having some trouble, Posted 3 months ago. Direct link to Teliyah Coletrain's post when you get negitive and, Posted 3 years ago. Use the slope formula [latex]m=\Large\frac{\text{rise}}{\text{run}}[/latex] to identify the rise and the run. Yes, it's positive. What is the best online graphing calculator? While x2 and y2 represent . This calculator will find the slope, y-intercept, and angle of a straight line when two points on the line are known. brah can sum1 help me I no understand um, Mahaloz, I can't understand how to graph an equation with a fraction y-intercept. Slope in a table. Here we have: Step 2: Identify the slope of line. Point-slope form is a form of a linear equation, where there are three characteristic numbers - two coordinates of a point on the line, and the slope of the line. If x1 is 2 and x2 is 5, that's +3, so you would write 3. Explore math with our beautiful, free online graphing calculator. Direct link to caydenpri44's post whos watching in 2023?, Posted 4 months ago. To go from seven to 13, we added six. Let's find how much the change in x aka the run is. A graph of a line intersects the points zero, negative three and one, negative one. Their slope is an important factor in how they take waste away from your house. As the slope intercept form is y=mx+c , the slope is m and y-intercept is c. Therefore the slope of y=7x+2 is 7 and y-intercept is (0, 2). Both of these points are plotted and labeled. Direct link to Zelda's post I may be asking a too adv, Posted 2 years ago. Graphing calculators are an important tool for math students beginning of first year algebra. Sometimes, we will be given one point and the slope of the line, instead of its equation. 2, slash, 3, space, start text, p, i, end text. This gives a second point of (0+4,2-3) or (4,-1) and (4+4,-1-3) or (8,-4) to draw a line. When we are given an equation in the slope-intercept form of [latex]y=mx+b[/latex], we can easily identify the slopeand y-intercept and graph the equation from this information. Graphing a line given point and slope. And you could of, you didn't Direct link to ashlee.j975's post I just don't understand t, Posted 2 years ago. Knowing the pitch is important in climates where there is heavy snowfall. So let's just pick two xy pairs here, and we can actually pick any two if we can assume that this is Starting at the point we plotted, count out the rise and run to mark the second point. By definition, the slope or gradient of a line describes its steepness, incline, or grade. But I just like to think of it as rise over run. Graph the line passing through the point [latex]\left(1,-1\right)[/latex] whose slope is [latex]m=\Large\frac{3}{4}[/latex]. Why do we calculate slope as y/x not x/y? As the slope increases, it makes sense to me that the line will get steeper and steeper (a slope of 2 should be more steep than a slope of 1). - [Instructor] We are asked, what is the slope of the line Both six and four are divisible by two, so let be divide both the just pick the first two. 1 3 / 4 1\ 3/4 13/4. x-intercepts and y-intercepts. How Do You Plot Points in the Coordinate Plane. What About y = mx + b ? To do that, we use the fact that in a slope of. 2.Standard form - this is the line of the form , where and are real numbers and A and B are both not zero Direct link to ramoschavez.dayrin's post I am having trouble under, Posted 3 years ago. (NOTE: it isimportant for the equation to first be in slope intercept form. Starting at the given point, count out the rise and run to mark the second point. In this tutorial, see how to use that given slope and point to graph the line. Use the slope formula to identify the rise and the run. run. What is change in y over change in x? Given m, it is possible to determine the direction of the line that m describes based on its sign and value: Slope is essentially the change in height over the change in horizontal distance, and is often referred to as "rise over run." To log in and use all the features of Khan Academy, please enable JavaScript in your browser. So start with the y intercept, and count the slope from that point. Connect the two points with a line. Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. To find the equation of a line given the slope, use the slope-intercept form of the equation of a line, which is given by: y = mx + b, where m is the slope of the line and b is the y-intercept. Lets look at a few now. A line is increasing, and goes upwards from left to right when m > 0, A line is decreasing, and goes downwards from left to right when m < 0, A line has a constant slope, and is horizontal when m = 0. For non-linear functions, the rate of change of a curve varies, and the derivative of a function at a given point is the rate of change of the function, represented by the slope of the line tangent to the curve at that point. Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line. Now use the slope to count up or down and over left or right to the next point. to go from two to three you're just adding one. [emailprotected]. When this happens, we use the definition of slope to draw the graph of the line. Starting at the given point, count out the rise and run to mark the second point. $y = mx + b$ where $m$ Please tell me how can I make this better. Mark the second point. even have to do this math, you would have been able to see to go from two to three you added one, and to go from four to one, Direct link to gjp100's post I don't have a clue on ho, Posted 2 years ago. Connect the two points with a line. ( , ) Example: (3,2) .and the slope of the line. Example Graph the line with y -intercept 2 whose slope is m = 2 3. Plot the given point, the [latex]y[/latex] -intercept [latex]\left(0,2\right)[/latex]. Donate or volunteer today! How do I graph a line if the slope isn't provided? To do that, we take . We can check our line by starting at any point and counting up [latex]3[/latex] and to the right [latex]4[/latex]. There are many ways to think about slope. So point (x1, y1) is actually (0, b) and the equation becomes: Start with y y1 = m (x . Step 1: Identify the coordinates. When this happens, we use the definition of slope to draw the graph of the line. Did you have an idea for improving this content? numerator and the denominator by two and we get three Graph a line given a point and a slope. The slope can be represented by m and the y-intercept, where it crosses the axis and [latex]x=0[/latex], can be represented by [latex](0,b)[/latex] where b is the value where the graph crosses the vertical y-axis.Any other point on the line can be represented by [latex](x,y . If you want to contact me, probably have some questions, write me using the contact form or email me on Graph the line with [latex]y[/latex] -intercept [latex]\left(0,2\right)[/latex] and slope [latex]m=-\Large\frac{2}{3}[/latex]. Answer: Slope m = 12 5 As a decimal: m = -2.4 Graph of the line y = mx + b 1 2 3 4 5 6 7 8 9 1 2 5 5 10 0,0 - o + X Y (2, 3) (7, -9) Graph tools will zoom, move and enter full screen mode. Learn how to graph lines whose equations are given in the slope-intercept form y=mx+b. You may already be familiar with the y=mx+b form (called the slope-intercept form of the equation of a line). So our slope is six fourths, and we could rewrite that if we like. x. Sometimes, we will be given one point and the slope of the line, instead of its equation. Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. if the slope is negative then your rise is negative, so you go down. when our change in x is four. The slope and y-intercept calculator takes a linear equation and allows you to calculate the slope and y-intercept for the equation. So, -x would be -1x or -1/1x. Direct link to owen.esparza's post ligma, Posted 2 years ago. Plot the given point, [latex]\left(1,-1\right)[/latex]. b is the y value of the y-intercept of the graph. Fill the point that the line passes through. X1 and y1 represent the first point of coordinates. Welcome to MathPortal. CC licensed content, Specific attribution, Mathematics for the Liberal Arts Corequisite, [latex]\Large\frac{\text{rise}}{\text{run}}\normalsize=\Large\frac{4}{1}[/latex], [latex]\text{rise}=4\text{ run}=1[/latex], [latex]m=\Large\frac{\text{rise}}{\text{run}}[/latex], [latex]m={\Large\frac{\text{9 ft}}{\text{18 ft}}}[/latex], The slope of the roof is [latex]{\Large\frac{1}{2}}[/latex], [latex]m={\Large\frac{-\frac{1}{4}\text{in}\text{.}}{1\text{ft}}}[/latex]. pick any two of these pairs in order to figure that out if we assume that this is indeed a line. Graph the line with [latex]y[/latex] -intercept [latex]\left(0,2\right)[/latex] and slope [latex]m=-\Large\frac{2}{3}[/latex]. its positive. A coordinate plane. The slope of a line is the steepness of the line. It makes most sense on a graph. And what's our change in y? I designed this website and wrote all the calculators, lessons, and formulas. IF you tried flipping it over, as the slope gets closer to the x axis, the slope would get bigger and bigger to reach infinite slope, and thus you would have an infinite slope between negative and positive slopes, but this too does not make sense because 0 is between negative and positive numbers. We should get to another point on the line. Plus, the calculator also finds the distance between the two entered points, formulates the equation of the line, and even shows its work as to how it arrived at the slope and the line equation. if you can figure it out or pause the video again and Another method we can use to graph lines is the point-slope method. Check out this tutorial to learn about slope! I am assuming you are saying that a -/- gives a positive which you are correct. ourselves what slope is. It is the same equation, in a different form! Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. We can plot the point by starting at the origin and counting down 4 to get to (0,-4) and put a dot at this point. Slope. y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f, start color #ed5fa6, m, end color #ed5fa6, start color #0d923f, b, end color #0d923f, y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, 3, end color #0d923f, start color #ed5fa6, 2, end color #ed5fa6, left parenthesis, 0, comma, start color #0d923f, 3, end color #0d923f, right parenthesis, left parenthesis, 0, start color #ed5fa6, plus, 1, end color #ed5fa6, comma, start color #0d923f, 3, end color #0d923f, start color #ed5fa6, plus, 2, end color #ed5fa6, right parenthesis, equals, left parenthesis, 1, comma, 5, right parenthesis, y, equals, start color #ed5fa6, start fraction, 2, divided by, 3, end fraction, end color #ed5fa6, x, start color #0d923f, plus, 1, end color #0d923f, left parenthesis, 0, comma, start color #0d923f, 1, end color #0d923f, right parenthesis, left parenthesis, 0, start color #ed5fa6, plus, 1, end color #ed5fa6, comma, start color #0d923f, 1, end color #0d923f, start color #ed5fa6, plus, start fraction, 2, divided by, 3, end fraction, end color #ed5fa6, right parenthesis, equals, left parenthesis, 1, comma, 1, start fraction, 2, divided by, 3, end fraction, right parenthesis, left parenthesis, 1, comma, 1, start fraction, 2, divided by, 3, end fraction, right parenthesis, start color #ed5fa6, start fraction, 2, divided by, 3, end fraction, end color #ed5fa6, start color #ed5fa6, 3, end color #ed5fa6, left parenthesis, 0, start color #ed5fa6, plus, 3, end color #ed5fa6, comma, start color #0d923f, 1, end color #0d923f, start color #ed5fa6, plus, 2, end color #ed5fa6, right parenthesis, equals, left parenthesis, 3, comma, 3, right parenthesis, y, equals, start fraction, 3, divided by, 4, end fraction, x, plus, 2, y, equals, minus, start fraction, 3, divided by, 2, end fraction, x, plus, 3, How come if the negative sign is next to the fraction it causes the rise to be negative but not the run. Solution The slope and the intercept are then combined to provide the equation of the line in slope intercept form ("y=mx+b"). Problem. Direct link to Sofia's post If you get negative and n, Posted 2 years ago. However, there exist different forms for a line equation. The coordinate plane has two axes: the horizontal and vertical axes. Direct link to Envy's post Not to be that person but, Posted 2 years ago. What is the required slope? Direct link to Timohi's post Im using the first exampl, Posted 3 years ago. If you're seeing this message, it means we're having trouble loading external resources on our website. What Does the Slope of a Line Mean? You have to see the difference between x/y point 1 and x/y point 2. Wed love your input. press esc to exit full screen mode Slope Solution m = r i s e r u n = y x Plot the given point. Mark the second point. Quiz 2: 5 questions Practice what you've learned, and level up on the above skills. Since x and y form a right triangle, it is possible to calculate d using the Pythagorean theorem. How to find slope Identify the coordinates (x_1, y_1) (x1 ,y1 ) and (x_2, y_2) (x2 ,y2 ). Interactive online graphing calculator - graph functions, conics, and inequalities free of charge Direct link to The Telepath's post Hi, Graph the line passing through the point [latex]\left(1,-1\right)[/latex] whose slope is [latex]m=\Large\frac{3}{4}[/latex]. CC licensed content, Specific attribution, [latex]\Large\frac{\text{rise}}{\text{run}}\normalsize=\Large\frac{4}{1}[/latex], [latex]\text{rise}=4\text{ run}=1[/latex], [latex]m=\Large\frac{\text{rise}}{\text{run}}[/latex], [latex]m={\Large\frac{\text{9 ft}}{\text{18 ft}}}[/latex], The slope of the roof is [latex]{\Large\frac{1}{2}}[/latex], [latex]m={\Large\frac{-\frac{1}{4}\text{in}\text{.}}{1\text{ft}}}[/latex]. Level up on all the skills in this unit and collect up to 1300 Mastery points! example Graph the line with y y -intercept (0,2) ( 0, 2) and slope m= 2 3 m = 2 3 Show Solution try it And what's our change in y? We already know that, Additionally, because the slope of the line is. Briefly: The above equation is the Pythagorean theorem at its root, where the hypotenuse d has already been solved for, and the other two sides of the triangle are determined by subtracting the two x and y values given by two points. Remember, "x" is the same as "1x". Learn about these axes and the name for their point of intersection by watching this tutorial! [latex]\begin{array}{}\\ \\ m=-\frac{2}{3}\hfill \\ \frac{\text{rise}}{\text{run}}=\frac{-2}{3}\hfill \\ \\ \\ \text{rise}=-2\hfill \\ \text{run}=3\hfill \end{array}[/latex]. x1 y1 as the starting point and x2 y2 as the ending point. As the slope increases, it makes sense to me that the line will get steeper and steeper (a slope of 2 should be more steep than a slope of 1). You can't learn about linear equations without learning about slope. Practice calculating the slope of a line given some points on the line shown in a table. This online calculator finds the equation of a line given two points on that line, in slope-intercept and parametric forms. so negative slope means either the rise goes down and run goes right OR rise goes up and run goes left. In technical terms, the slope of the line is the change in y over the change in x. Here you can find two calculators for an equation of a line: It also outputs slope . Direct link to David Severin's post It makes most sense on a , Posted 8 months ago. Sometimes you would see Knowing how to plot ordered pairs is an essential part of graphing functions. So, the slope of the equation is 1 and the y-intercept is (0,4). Direct link to 682060's post How come if the negative , Posted 5 years ago. that contains these points? Solution Slope from two points . [latex]\begin{array}{}\\ \\ m=\frac{3}{4}\hfill \\ \frac{\text{rise}}{\text{run}}=\frac{3}{4}\hfill \\ \\ \\ \text{rise}=3\hfill \\ \text{run}=4\hfill \end{array}[/latex]. So if you have y=3x-4, the slope is 3=3/1, the y intercept is (0,-4). The slope can be represented by m and the y-intercept, where it crosses the axis and [latex]x=0[/latex], can be represented by [latex](0,b)[/latex] where b is the value where the graph crosses the vertical y-axis. the information we need. This formula is known as the slope-intercept equation. Write the equation of the line in the graph by identifying the slope and y-intercept. Because -3/2 is basically equal to minus 3 by PLUS 2, im having some trouble anybody have some helpful tips hehehe. Slope-Intercept Form. Direct link to mukhopadhyayaveri14's post I can't understand how to, Posted 2 months ago. Direct link to wesley jones's post i don't really get it why, Posted 4 years ago. Use the slope formula to identify the rise and the run. Think you need to find an equation first? Solution The first thing to realize is that each solution is a point on the line. Any other point on the line can be represented by [latex](x,y)[/latex]. So we're going from two to three, so our change in x is The calculator given in this section can be used to find the equation of a line when a point on the line and its slope are given. A graph of a line intersects the points zero, negative three and one, negative one. You might need: Calculator. Not to be that person but like When am I reallyyyyyyyyyyyy going to use this in everyday life? Starting at [latex]\left(0,2\right)[/latex], count the rise and the run and mark the second point. Graph the line passing through the point [latex]\left(-1,-3\right)[/latex] whose slope is [latex]m=4[/latex]. Here's a table if you need help: I may be asking a too advanced question but how to we solve if our numbers on our table are. It's positive. Direct link to The Telepath's post Yes, it's positive. Graph the line with [latex]y[/latex] -intercept [latex]\left(0,2\right)[/latex] and slope [latex]m=-\Large\frac{2}{3}[/latex]. If you start with s slope of 1, it is at a 45 degree angle where y=x. What is the slope of the line? Use the slope formula [latex]m=\Large\frac{\text{rise}}{\text{run}}[/latex] to identify the rise and the run. Similarly, subtract the x-value one point from the x-value of another. The slope formula is simply the change in y over the change in x: Slope = m =. Think about the fraction as division How do you get a negative number when dividing: i don't really get it why in the last exercise the slope is -3/2 you ad plus 2 for the change in x but minus 3 for the change in y. Direct link to micahwbeninghove's post I'm am., Posted 3 months ago. }}}[/latex], The slope of the pipe is [latex]-{\Large\frac{1}{48}}[/latex], Graph a line given the slope and a point on the line. [latex]\begin{array}{}\\ \\ m=\frac{3}{4}\hfill \\ \frac{\text{rise}}{\text{run}}=\frac{3}{4}\hfill \\ \\ \\ \text{rise}=3\hfill \\ \text{run}=4\hfill \end{array}[/latex].