What is the rate of change for the function shown in the given graph?
In order to find the rate of change, we need to take the change in 𝑦-values and divide by the change in 𝑥-values. So let’s pick up two points on the graph, here and here. So before finding this, when looking at our change in the 𝑦-values, going up will be positive for 𝑦. And going down, would be negative for 𝑦. For 𝑥, going to the right would be positive for 𝑥. And going to the left would be negative for 𝑥. So when we go from point to point, we need to go left to right. So our leftmost point would be here.
So we need to go up or down. We need to go up two. So our change in 𝑦 is two. And then, we need to go right one. That’s positive one for 𝑥.
Therefore, our rate of change would be two over one. It’s also good to know that this rate of change will be the same as the slope.