Question

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apoline is mowing lawns for a summer job. for every mowing job, she charges an initial fee plus a constant fee for each hour of work. her fee for a 5 - hour job, for instance, is $42. her fee for a 3 - hour job is $28.
let y represent apollines fee (in dollars) for a single job that took x hours for her to complete.
which of the following information about the graph of the relationship is given?
choose 1 answer:
slope and x - intercept
slope and y - intercept
slope and a point that is not an intercept
x - intercept and y - intercept
y - intercept and a point that is not an intercept
two points that are not intercepts
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slope and intercept meaning in context
slope, x - intercept, y - intercept meaning in context

Explanation:

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given two points \((x_1,y_1)=(3,28)\) and \((x_2,y_2)=(5,42)\).
\(m=\frac{42 - 28}{5 - 3}=\frac{14}{2}=7\)

Step2: Analyze the nature of the points

The points \((3,28)\) and \((5,42)\) are not intercepts (since when \(x = 0\), \(y\) is not \(28\) or \(42\) and when \(y=0\), \(x\) is not \(3\) or \(5\)). We have found the slope (from the two - point formula) and we have two non - intercept points.

Answer:

F. Two points that are not intercepts