Mathematics

Question

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.

2 Answer

  • well the equation I got is 32x +80 = y
    x representing how many hours and y representing how much money the electrician is gonna get from that job
  • Answer:

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

    Step-by-step explanation:

    Givens

    • An electrician charges $80 plues $32 per hour.

    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.

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