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?

Question

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?

Bytelearn · Accepted Answer

Identify Charges:  Step 1: Identify the charges for different hours worked. Apolline charges $42 for a 5-hour job and $28 for a 3-hour job. Calculate Hourly Rate:  Step 2: Calculate the hourly rate. To find the hourly rate, we can use the equation for a line, y = mx + b, where m is the slope and b is the y-intercept. Here, y represents the total fee, and x represents the hours worked. First, calculate the slope (m) which is the rate per hour: m = (Change in y) / (Change in x) = ($42 - $28) / (5 hours - 3 hours) = $14 / 2 hours = $7 per hour. Calculate Initial Fee:  Step 3: Calculate the initial fee (y-intercept, b). Using one of the points, say (3, $28), and the slope from Step 2: $28 = $7(3) + b $28 = $21 + b b = $28 - $21 = $7. Write Equation:  Step 4: Write the equation of the line. The equation representing the relationship between hours worked (x) and the fee charged (y) is: y = 7x + 7. Determine Graph Information:  Step 5: Determine the information about the graph. The equation y = 7x + 7 is a linear equation, which means the graph is a straight line. The slope of the line is 7, indicating that the fee increases by $7 for each additional hour worked. The y-intercept is $7, meaning the initial fee before any hours are worked is $7.

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