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

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

We can use the formula y = mx + b, where m is the slope and b is the y-intercept.

We know that when Esperanza worked 6 hours, she earned $120. So we have the point (6, 120).

We also know that when Esperanza worked 8 hours, she earned $156. So we have the point (8, 156).

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

m = (156 - 120) / (8 - 6)

m = 36 / 2

m = 18

Now we can substitute the slope and one of the points into the equation to solve for b.

120 = 18(6) + b

120 = 108 + b

b = 120 - 108

b = 12

Therefore, the equation of the linear function is:

y = 18x + 12