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Algebra / Linear functions Difficulty: Medium

The graph represents the total charge, in dollars, by an electrician for $x$ hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

The electrician’s hourly rate

The electrician’s onetime fee

The maximum amount that the electrician charges

The total amount that the electrician charges

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Explanation

Choice A is correct. It’s given that the electrician charges a onetime fee plus an hourly rate. It's also given that the graph represents the total charge, in dollars, for $x$ hours of work. This graph shows a linear relationship in the xy-plane. Thus, the total charge $y$ , in dollars, for $x$ hours of work can be represented as $y = m x + b$ , where $m$ is the slope and $left parenthesis 0 comma b right parenthesis$ is the y-intercept of the graph of the equation in the xy-plane. Since the given graph represents the total charge, in dollars, by an electrician for $x$ hours of work, it follows that its slope is $m$ , or the electrician’s hourly rate.

Choice B is incorrect. The electrician's onetime fee is represented by the y-coordinate of the y-intercept, not the slope, of the graph.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.