An electrician charges $80 plus $32 per hour. Write an equation that represents the total fee y (in dollars) charged by the electrician for a job lasting x hours. Find the x and y intercepts. Is the value of the x intercept applicable to the electrician? Explain. Thank you to whoever answers this question, I am not asking this to cheat off of homework, but to understand the answer for what I am doing. Learning from it.

Now, according to the problem, the electrician charges initially $80, that's a constant, it's not related with the number hours, that means it's the initial condition, the constant term.

Then, he charges $32 per hour, that is, this charge depends on the number of hours, it's variable. In other words, it represents a ratio of change.

So, if we apply all this to an equation, it would be

[tex]y=mx+b[/tex]

Where, [tex]m[/tex] is the ratio of change, [tex]b[/tex] is the initial condition (y-intercept), [tex]x[/tex] is time and [tex]y[/tex] is money.

Therefore, the equation which models this situation is

[tex]y=32x+80[/tex]

The y-intercept is for [tex]x=0[/tex]

[tex]y=32(0)+80=80[/tex]

The x-intercept is for [tex]y=0[/tex]

[tex]0=32x+80\\x=\frac{-80}{32}= -2.5[/tex]

Observe that x-intercept is at (-2.5,0), which doesn't make sense to the problem, because time cannot be negative.