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).

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

From the given information:
Point 1: (6, 120)
Point 2: (8, 156)

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

Now, we can use the point-slope formula to find the y-intercept:
y - y1 = m(x - x1)
y - 120 = 18(x - 6)
y - 120 = 18x - 108
y = 18x + 12

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