Question

Example 4

15. PLUMBER Two neighbors, Camila and Conner, hire the same plumber for
household repairs. The plumber worked at Camila's house for 3 hours and
charged her $191. The plumber worked at Conner's house for 1 hour and
charged him $107.
a. Define variables to represent the situation.
b. Find the slope and y-intercept. Then, write an equation.
c. How much would it cost to hire the plumber for 5 hours of work?

Answer 1

The independent variable is the hours worked by the plumber, and the dependent variable is the cost charged. The equation is y = 42x + 191. The cost for 5 hours of work is $401.

Step-by-step explanation:

The independent variable in this situation is the hours worked by the plumber, and the dependent variable is the cost charged by the plumber.

a. Let x represent the number of hours worked and y represent the cost charged by the plumber.
b. To find the slope, we can use the formula: slope = (change in y) / (change in x). The change in y is the difference in cost charged by the plumber, which is $107 - $191 = -$84. The change in x is the difference in hours worked, which is 1 - 3 = -2. So, the slope is -84 / -2 = 42. The y-intercept is the cost charged when x = 0, which is $191. The equation is y = 42x + 191.
c. To find the cost for 5 hours of work, we can plug in x = 5 to the equation: y = 42(5) + 191 = 210 + 191 = $401.

Answer 2

Answer: Part a: b represents the base fee charged for the "house call" job

m is the hourly rate.

x is the number of hours at the job.

y represents the total cost for the job.

Part b:. The y-intercept is 65

The equation follows y=mx+b

Y= 42x + 65

Part c:. $275

Step-by-step explanation:

The difference between the two total costs, (Camilla 191 - Connor 107)

= $84. That is the rise. The run is the difference in time, 2 hours. 84/2 = 42.

m= 42

42 from 107 to find b, the base fee, 65 This is the y-intercept.

The equation is y= 42x + 65

Quick check using Camilla's bill: 191 = (42)(3) + 65

191 = 126 + 65 True!

Part C:

To find the total cost of the plumber's 5 hour job,

Y = 42(5) + 65

Y= 210 + 65

Y= $275