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)
Let x be the number of hours Esperanza works and y be the amount of money she earns.
We are given two points on the line: (6, 120) and (8, 156).
Using the slope formula, we can find the slope (m) of the line:
m = (y2-y1)/(x2-x1) = (156-120)/(8-6) = 36/2 = 18
Now we can use the slope-intercept form of a linear equation, y=mx+b, to find the y-intercept (b):
Using one of the given points (6, 120):
120 = 18(6) + b
120 = 108 + b
b = 12
So the equation of the linear function that models the relationship between the number of hours Esperanza works (x) and the amount of money she earns (y) is:
y = 18x + 12