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)
Let's use the slope-intercept form of a linear function, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (change in y)/(change in x) = (earnings)/(hours worked)
For Esperanza, the slope is (156 - 120)/(8 - 6) = 36/2 = 18.
Now, let's find the y-intercept.
We know that when Esperanza worked for 6 hours, she earned $120. Using the y-intercept form, substitute 6 for x and 120 for y, and solve for b:
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Thus, 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