Write the function that is represented by the graph.
If we think about the 𝑦-intercept form, 𝑦 equals 𝑚𝑥 plus 𝑏, we need the slope of the line and the 𝑦-intercept to write its function. The 𝑦-intercept is the place where the line crosses the 𝑦-axis.
Notice here that the 𝑦-axis is being called 𝑓 of 𝑥, the function of 𝑥. We can also say 𝑓 of 𝑥 equals 𝑚𝑥 plus 𝑏.
But back to the 𝑦-intercept. The place where it crosses the 𝑦-axis on this graph is three. 𝑓 of 𝑥 equals the slope times 𝑥 plus three.
To find the slope, let’s consider the changes in 𝑦 over the changes in 𝑥.
Here’s an example. As we go down two from three, so down two on the 𝑦-axis, we go over three on the 𝑥-axis. Down two, right three gives us a slope of negative two-thirds. And we’ve already considered that the 𝑦-intercept is three.
The function represented by this graph is 𝑓 of 𝑥 equals negative two-thirds 𝑥 plus three.