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.
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