On two separate occasions, Mr. Johnson needed some electrical work done on his house. He called an electrician from Electrical Outlet in town. The electrician worked 2.5 hours and charged $180 for the first visit. The second time he worked 4 hours and charged $243. Let be the number of hours the electrician works in a single visit, and let be the total amount, in dollars, that the electrician charged for the visit. A. Create the equation that relates the total cost to the time worked. [4 pts] Note: This will be a linear relationship, so start by finding the slope of the line based on the given information. Express the final equation in = + form.

y = 42x + 75

Step-by-step explanation:

Using the equation of a line in the form

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁) = m where m is the slope of the line

Let x be the number of hours the electrician works in a single visit, and let y be the total amount, in dollars, that the electrician charged for the visit.

Since the electrician worked 2.5 hours and charged $180 for the first visit. The second time he worked 4 hours and charged $243. where x₁ = 2.5 hours, y₁ = $ 180, x₂ = 4 hours and y₂ = $ 243

We find the slope of the line, m

m = (243 - 180)/(4 - 2.5) = (243 - 180)/(4 - 2.5) = 63/1.5 = 42

Since m = (y - y₁)/(x - x₁) ,

42 = (y - 180)/(x - 2.5)

cross-multiplying, we have

42(x - 2.5) = (y - 180)

expanding the bracket, we have

42x - 105 = y - 180

adding 180 to both sides, we have

42x - 105 + 180 = y - 180 + 180

42x + 75 = y

y = 42x + 75