Apolline 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 Apolline's 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: (A) Slope and x-intercept (B) Slope and y-intercept (C) Slope and a point that is not an intercept (D) x-intercept and y intercept (E) y-intercept and a point that is not an intercept (F) Two points that are not intercepts

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Apolline 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 Apolline's 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: (A) Slope and  x-intercept (B) Slope and  y-intercept (C) Slope and a point that is not an intercept (D)  x-intercept and  y intercept (E)  y-intercept and a point that is not an intercept (F) Two points that are not intercepts

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Define Variables: Let's denote the initial fee that Apolline charges as $ b $ (which will be the y-intercept of the graph) and the constant fee per hour as $ m $ (which will be the slope of the graph). We can then express Apolline's fee for a job as $ y = mx + b $, where $ y $ is the total fee and $ x $ is the number of hours worked.Calculate Slope: We are given two points: (5, 42) for a 5-hour job and (3, 28) for a 3-hour job. These points can be used to find the slope $ m $ of the graph. The slope $ m $ is calculated by the change in $ y $ divided by the change in $ x $, which is $ (42 - 28) / (5 - 3) $.Find Y-Intercept: Performing the calculation for the slope $ m $, we get $ m = (42 - 28) / (5 - 3) = 14 / 2 = 7 $. So, Apolline charges $7 per hour of work.Determine Initial Fee: Now that we have the slope $ m $, we can use one of the points to find the y-intercept $ b $. Let's use the point (5, 42). Plugging these values into the equation $ y = mx + b $, we get $ 42 = 7(5) + b $.Describe Graph: Solving for $ b $, we have $ 42 = 35 + b $, which gives us $ b = 42 - 35 = 7 $. Therefore, the initial fee that Apolline charges is $7.Identify Given Information: With the slope $ m = 7 $ and the y-intercept $ b = 7 $, we have enough information to describe the graph of the relationship. The slope corresponds to the constant fee per hour, and the y-intercept corresponds to the initial fee.The question asks which of the following information about the graph is given. We have determined both the slope and the y-intercept from the information provided. Therefore, the correct answer is (B) Slope and y-intercept.

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