To determine which equation has a smaller rate of change than what is shown in the graph, we need to compare the coefficients of the variable x in each equation.
The given graph is not provided, so we cannot directly analyze the rate of change from the graph itself. However, we can compare the coefficients of x in the given equations to determine their rates of change.
A. y = 65x + 100
The coefficient of x is 65, indicating that the rate of change is 65.
B. y = 85x
The coefficient of x is 85, indicating that the rate of change is 85.
C. y = 50x + 150
The coefficient of x is 50, indicating that the rate of change is 50.
Comparing the coefficients, we can see that the equation with the smallest rate of change is option C: y = 50x + 150.
Therefore, the correct answer is C.