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 Esperanza worked in the amount of money she earns enter your answer in y = mx + b form

Answer 1

To find the equation of the linear function, we can use the point-slope formula:

Let the number of hours Esperanza worked be x and the amount of money she earned be y.

Using the points (6, 120) and (8, 156) to find the slope:
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18

Now, plug one of the points into the slope-intercept form y = mx + b to find the y-intercept b:

120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12

Therefore, the linear function that models the relationship between the number of hours Esperanza worked and the amount of money she earned is:

y = 18x + 12