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 determine the slope (m) and the y-intercept (b).

Let x represent the number of hours worked and y represent the amount of money earned.

Using the given data:
(6, 120) and (8, 156)

First, calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18

Now substitute one of the points and the slope into the equation y = mx + b to find the y-intercept:
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12

Therefore, the equation of 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