Equations of Linear Functions Practice

Question

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Question
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.(1 point)

Answer 1

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

We are given two points on the line: (6, 120) and (8, 156).

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

Now that we have the slope, we can use one of the points to find the y-intercept. Let's use (6, 120).
Using the slope-intercept form y = mx + b:
120 = 18(6) + b
120 = 108 + b
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.