Stephanie volunteered at the 5k being held at the park near her home. The chart below gives the number of hours Stephanie worked and the total number of runners that passed by her.

Hours (h) Runners (r)
1

150
2 300
3 450
4 600
Based on the table, write an equation for the relationship between the number of hours Stephanie worked and the number of runners that passed her.

(1 point)
Responses

r = h150
r = h150

r = 150h
r = 150h

r = 150h
r = 150h

r = 150 + h

1 answer

To determine the equation for the relationship between the number of hours Stephanie worked (h) and the number of runners (r) that passed her, we can observe the data provided in the chart.

From the chart:

  • For 1 hour (h = 1), 150 runners (r = 150)
  • For 2 hours (h = 2), 300 runners (r = 300)
  • For 3 hours (h = 3), 450 runners (r = 450)
  • For 4 hours (h = 4), 600 runners (r = 600)

We can see that for every hour worked, the number of runners increases by 150. This indicates a linear relationship.

The general form of a linear equation is:

\[ r = mh + b \]

where \( m \) is the slope (the rate of change) and \( b \) is the y-intercept. In this case, there is no intercept since when h = 0, r = 0.

The slope \( m \) can be determined as follows:

  • Since the number of runners increases by 150 for each hour, we have \( m = 150 \).

Thus, the equation for the relationship is:

\[ r = 150h \]

Therefore, the correct response is:

r = 150h