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)
In this case, we can represent the relationship between the number of hours worked (x) and the amount of money earned (y) with the equation:
y = mx + b
where:
m = the rate at which Esperanza earns money per hour
b = the starting amount of money earned (when x = 0)
To find the values of m and b, we can use the information provided:
When x = 6 (number of hours worked) and y = 120 (amount of money earned):
120 = 6m + b
When x = 8 (number of hours worked) and y = 156 (amount of money earned):
156 = 8m + b
Now we have a system of two equations with two variables:
6m + b = 120
8m + b = 156
Subtracting the first equation from the second equation:
(8m + b) - (6m + b) = 156 - 120
2m = 36
m = 18
Substitute m = 18 back into one of the original equations to solve for b:
6(18) + b = 120
108 + b = 120
b = 12
Therefore, 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