What equation represents the line shown?
The equation of a line is 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is the slope of the line and 𝑏 is the 𝑦-intercept. So what is the slope and the
𝑦-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 it’s essentially the rise over the run.
Now if we had two points on this graph, we could find it algebraically and subtract the 𝑦s and divide by
subtracting the 𝑥s. But since we’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 𝑦-intercept; that’s where you cross the 𝑦-axis. So
that part is pretty easy.
Let’s go ahead and find where we cross the 𝑦-axis. We cross it at five. Now next
is our slope. Okay, we can look anywhere on this graph and say, “okay, let’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.” So here we’ve- we’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 let’s go ahead and plug these in. So the equation of this line
would be 𝑦 equals one-half 𝑥 plus five. We could rewrite this and have 𝑦 equals 𝑥 over two plus
five. Instead of putting one-half times 𝑥, we can actually multiply this together and make it 𝑥
over two; however, either equation would be correct.