Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns.

Question

Enter your answer in y = mx + b form

Answer 1

Let x represent the number of hours Esperanza works and y represent the amount of money she earns.

We can create two points from the given information:
(6, 120) and (8, 156)

First, find the slope (m):
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18

Next, use one of the points to find the y-intercept (b). Let's use (6, 120):
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12

Therefore, the equation of the linear function that models the relationship is:
y = 18x + 12