Respuesta :
Answer:
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
The linear equation that relates the total cost to the time worked is:
[tex]y = 42x + 75[/tex]
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
In this problem, the function has two points: (2.5, 180) and (4, 243).
The slope is given by change in y divided by change in x, hence:
[tex]m = \frac{243 - 180}{4 - 2.5} = 42[/tex]
Then:
[tex]y = 42x + b[/tex]
Considering point (2.5, 180), we have that when x = 2.5, y = 180, which is used to find b.
[tex]y = 42x + b[/tex]
[tex]180 = 42(2.5) + b[/tex]
[tex]b = 75[/tex]
Hence, the function is:
[tex]y = 42x + 75[/tex]
More can be learned about linear equations at https://brainly.com/question/24808124
