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. Enter your answer in y=mx+b form

Answer 1

To find the equation of the linear function, we first need to find the slope (m) and the y-intercept (b).

First, let's find the slope:
Slope (m) = (change in y) / (change in x)
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18

Now, let's find the y-intercept (b) using one of the points (6, 120):
y = mx + b
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12

Therefore, the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns is:
y = 18x + 12