Which of the following describes the equation of the straight line shown in the figure? A) 𝑦 equals negative two 𝑥 minus two. B) 𝑦 equals negative two 𝑥 plus one. C) 𝑦 equals two 𝑥 minus one. Or D) 𝑦 equals negative two 𝑥 plus two.
We are trying to find the equation of the straight line. And the equation of any line can be represented by 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is the slope and 𝑏 is the 𝑦-intercept, where the line crosses the 𝑦-axis. So first of all, what is a slope? It’s looking at the line and deciding how it’s changing vertically over how it’s changing horizontally. So the change in the 𝑦-values divided by the change in the 𝑥-values, sometimes denoted as the rise over the run. And as we said before, the 𝑦-intercept is where we cross the 𝑦-axis, located here.
So let’s begin with 𝑏, the 𝑦-intercept. We cross the 𝑦-axis here, at two. So our 𝑦-intercept will be positive two. Now, to find a slope, we need to find another point of intersection with the grid that this line has, here. So if we go left to right, how do we change vertically. Well, we go down two. So that’s negative two for 𝑦. And then we divide by the horizontal change, which is one. It’s in the positive direction for 𝑥. So our slope is negative two over one. Or ,simplifying that, negative two divided by one is negative two. So we need to replace 𝑚 with negative two and replace 𝑏 with positive two.
So the equation of this line will be 𝑦 equals negative two 𝑥 plus two, making D our answer.