Answer
a. Rate of change $\frac{1}{2}$
b. f(x) = $\frac{1}{2}$x - 1
Work Step by Step
a. The rate of change is how much y-increases for every one increase in the x value. Use the slope formula: $\frac{y_{2}-y_{1}}{x_{2}-x_{2}}$. Pick two points from the graph and plug them into the formula to get $\frac{1}{2}$ as the slope = rate of change.
b. The rate of change = a and the y-intercept = b. The y-intercept occurs when x = 0, which means that, based off the graph given, b (the y-intercept) = -1. So the overall equation for the function is f(x) = $\frac{1}{2}$x -1
