Question

donovan cleans houses. he charges $25 plus $15 per hour. which graph represents how much donovan charges to clean a house.

Explanation:

Step1: Define the cost function

Let \( h \) be the number of hours and \( C \) be the total cost. The fixed charge is \$25, and the variable charge is \$15 per hour. So the cost function is \( C = 15h + 25 \).

Step2: Analyze the y-intercept

When \( h = 0 \) (no hours worked), the cost is the fixed charge. Substitute \( h = 0 \) into the cost function: \( C = 15(0) + 25 = 25 \). So the graph should have a y-intercept at \( (0, 25) \).

Step3: Analyze the slope and a point

The slope of the line is 15 (the rate per hour). Let's check a point. For \( h = 1 \), \( C = 15(1) + 25 = 40 \). Wait, but looking at the options, option D has a y-intercept at \( (0, 25) \), which matches our y-intercept calculation. Let's verify the other options:

• Option A: y-intercept at \( (0, 15) \), which is incorrect (should be 25).
• Option B: y-intercept at \( (0, 0) \), incorrect.
• Option C: y-intercept near 0 or a point \( (1, 35) \), but \( 15(1)+25 = 40 \), not 35.
• Option D: y-intercept at \( (0, 25) \), which matches our cost function's y-intercept. Then, for \( h = 1 \), \( C = 40 \), and as \( h \) increases, the line has a slope of 15, which is consistent with the cost function.

Answer:

D. The graph with y-intercept (0, 25) (the last graph labeled D)