sterday, 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)
To find 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), we can first find the slope (m) using the first set of data points (6 hours, $120) and then use the slope to find the y-intercept (b).
First, find the slope:
m = (y2 - y1) / (x2 - x1)
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18
Now that we have the slope, we can use one of the data points and the slope to find the y-intercept (b). Let's use the first set of data points (6 hours, $120):
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Now that we have the slope (m) and the y-intercept (b), we can write the equation in y=mx+b form:
y = 18x + 12
So, the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns is y = 18x + 12.