Answer
a. Rate of change = -3
b. f(x) = -3x + 2
Work Step by Step
a. The rate of change is how much y-increases for every one increase in the x value. Since the x values do not increase by one in the chart one can use the slope formula: $\frac{y_{2}-y_{1}}{x_{2}-x_{2}}$. Pick two points from the table and plug them into the formula to get -3 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 chart given, b (the y-intercept) = 2. So the overall equation for the function is f(x) = -3x + 2
