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A student makes money by watching the neighbors' dog. The situation is modeled in the graph below.

Money Made
Fee (dollars): y axis numbers below
130
120
110
100
90
80
70
60
50
40
30
20
10
0 1 2 3 4 5 6 7 8 9 10
Time (days): x axis numbers above
The line has a positive slope and begins at (0, 20) on the y axis and and stops at (10,120)
Which statement correctly describes the relationship between the amount of money the student makes and time in days?
A. The student charges $11 plus an additional $20 per day.
B. The student charges $20 plus an additional $11 per day.
C. The student charges $10 plus an additional $20 per day.
D. The student charges $20 plus an additional $10 per day.

1 answer

To analyze the relationship between the amount of money the student makes and time in days, let's look at the given information.

  1. The starting point (y-intercept) is at (0, 20). This means that at 0 days, the student has made $20. This indicates that the student starts with a base fee of $20.

  2. The endpoint is at (10, 120). This means that after 10 days, the student has made a total of $120.

  3. To find the rate at which the student earns money per day, we can calculate the slope of the line using the two points (0, 20) and (10, 120):

    • Change in money made = 120 - 20 = 100 dollars
    • Change in time = 10 - 0 = 10 days

    So, the slope (which represents the amount earned per day) is: \[ \text{slope} = \frac{100}{10} = 10 \text{ dollars per day} \]

Putting this all together, we can construct the equation for the amount of money made (y) in terms of the number of days (x):

\[ y = 10x + 20 \]

From this equation, it is clear that:

  • The student charges a flat fee of $20 (the y-intercept).
  • The student earns an additional $10 for each day (the slope).

Based on these calculations, the correct statement describing the relationship is:

D. The student charges $20 plus an additional $10 per day.