Answer :
Answer:
[tex]C(x)=35x+50[/tex]
Electrician's fee: $50.
Charges per hour: $35
Step-by-step explanation:
Let x represent number of hours and y represent amount charged.
We have been given that an electrician charges $120 after 2 hours of work and $190 after 4 hours of work.
We can represent this information with two points as (2,120) and (4,190).
First of all, we will find slope using these points.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{190-120}{4-2}[/tex]
[tex]m=\frac{70}{2}[/tex]
[tex]m=35[/tex]
Now, we will slope-intercept form of equation [tex]y=mx+b[/tex] to get our required equation as:
[tex]y=35x+b[/tex]
Substitute coordinates of point (2,120) to find the y-intercept.
[tex]120=35(2)+b[/tex]
[tex]120=70+b[/tex]
[tex]120-70=70-70+b[/tex]
[tex]50=b[/tex]
Therefore, our required function would be [tex]C(x)=35x+50[/tex].
The electrician's fee would be $50 as it the initial amount or y-intercept.
The electrician charges $35 per hour as the slope of the line is 35.