Math - Linear Relationships - Equations

Question

Walton's Roof Installation and Repair charges a service call fee and an hourly rate for residential repairs. If a 7 hour repair costs $385 and a 6 hour repair costs $341, find a linear model for the relationship between the hours spent on a repair and the total charges of a repair. Let t represent the number of hours it takes to complete the repair and C represent the cost of the repair.

C=  

Answer 1

You have two data points. The first one (x₁,y₁) = (7,385) and the second (x₂,y₂) = (6,341). The slope of the line is m = rise/run = Δy/Δx = (385-341)/(7-6) = 44.

The equation for the line is (y - y₀) = m(x - x₀). You can choose either point for (x₀,y₀).

So, y - 385 = 44(x - 7). Reducing this gives: y = 44x + 77. Or, in terms of the variables of the problem,

C = 44t + 77. The y-intercept, 77 represents the service call fee.