David is riding his bike. The number of revolutions (turns) his wheels make varies directly with the distance he travels. See the graph below.

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(a) How many revolutions does David make per foot of distance traveled?
revolution(s)
(b) What is the slope of the graph?

Answer 1

To answer the questions, we will use the information from the provided graph.

(a) To find the number of revolutions David makes per foot of distance traveled, we first need to look at the values from the graph. We can choose two points on the line (for example, (10, 2) and (80, 16)).

• The first point: at \(x = 10\), the number of revolutions \(y = 2\).
• The second point: at \(x = 80\), the number of revolutions \(y = 16\).

The formula for the slope (change in \(y\) over change in \(x\)) gives us the ratio of revolutions to distance.

To find the number of revolutions per foot of distance traveled:

• The change in \(y\) (revolutions) from point 1 to point 2 is: \(16 - 2 = 14\) revolutions.
• The change in \(x\) (distance traveled) is: \(80 - 10 = 70\) feet.

Now, to find revolutions per foot: \[ \text{Revolutions per foot} = \frac{\text{Change in revolutions}}{\text{Change in distance}} = \frac{14 \text{ revolutions}}{70 \text{ feet}} = \frac{1}{5} \text{ revolutions per foot}. \]

Answer for (a): David makes \(\frac{1}{5}\) revolutions per foot of distance traveled.

(b) The slope of the graph is calculated using the same two points we identified earlier:

The slope (\(m\)) can be calculated as: \[ m = \frac{\Delta y}{\Delta x} = \frac{16 - 2}{80 - 10} = \frac{14}{70} = \frac{1}{5}. \]

Answer for (b): The slope of the graph is \(\frac{1}{5}\).