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Video: Identifying the Equation of a Graphed Straight Line

Bethani Gasparine

Which equation represents the line shown?<Figure>

02:30

Video Transcript

What equation represents the line shown?

The equation of a line is ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘, where ๐‘š is the slope of the line and ๐‘ is the ๐‘ฆ-intercept. So what is the slope and the ๐‘ฆ-intercept? In a line, the slope is a number that describes both the direction and the steepness of a line. So we can think of it as how far the line is moving up and down divided by how far the line is moving left and right. So itโ€™s essentially the rise over the run.

Now if we had two points on this graph, we could find it algebraically and subtract the ๐‘ฆs and divide by subtracting the ๐‘ฅs. But since weโ€™ve actually have the line, we can actually just find, looking at the graph, how much we went up or down and divide by how much we went left or right. Going up would be positive, going down would be negative, going to the right would be positive, and going to the left would be negative. Next is the ๐‘ฆ-intercept; thatโ€™s where you cross the ๐‘ฆ-axis. So that part is pretty easy.

Letโ€™s go ahead and find where we cross the ๐‘ฆ-axis. We cross it at five. Now next is our slope. Okay, we can look anywhere on this graph and say, โ€œokay, letโ€™s look at a point and then see how much we had to rise over how much we had to run to get to another point on the-on the line that we have.โ€ So here weโ€™ve- weโ€™re already looking at a point and we can look at another point. So here we have two points; they went exactly through a point on this graph.

Now we have to be careful though; every single dash line represents half of a point. So we actually went up one to get to six. And then we had to go to the right, two. So our rise was one and our run was two. So one-half is our slope. So letโ€™s go ahead and plug these in. So the equation of this line would be ๐‘ฆ equals one-half ๐‘ฅ plus five. We could rewrite this and have ๐‘ฆ equals ๐‘ฅ over two plus five. Instead of putting one-half times ๐‘ฅ, we can actually multiply this together and make it ๐‘ฅ over two; however, either equation would be correct.