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?

a). Let the fixed cost charged by the plumber = $b

   And hourly amount charged by the plumber = $m per hour

   Therefore, linear equation representing the amount 'y' charged by the

   plumber will be,

   y = mx + b

   Here, two variables are,

  x = hours worked by the plumber

   y = Total amount charged by the plumber

b). If we graph the equation,

   Two ordered pairs (3, 191) and (1, 107) will lie on the line.

   Substitute the values of the given ordered pairs in the equation,

   For (3, 191),

   191 = 3m + b (1)

   For (1, 107),

   107 = m + b (2)

   Subtract equation (2) from (1),

   191 - 107 = (3m + b) - (m + b)

    84 = (3m - m) + (b - b)

    84 = 2m

    m = 42

    Substitute the value of 'm' in the equation (2),

    107 = 42 + b

    b = 65

   Therefore, slope of the equation is '42' and y-intercept of the equation

   is '65'.

    Equation for this situation will be,

    y = 42x + 65

C). If x = 5 hours,

     y = 42(5) + 65

     y = $275

     Therefore, it will cost $275 to hire the plumber.

     Learn more,

     link

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

step-by-step explanation:

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step-by-step explanation: