The graph shows a proportional relationship between the number of miles and the number of hours Marco bikes.

Question

What equation relates the distance, y, and the time, x? Enter your answer in the box.

Marcos biking graph showing miles on the y axis and hours on the x axis. A line begins at the origin and passes through the points 1 comma 15, 3 comma 45, and 5 comma 75.

y =
x

Answer 1

To determine the equation that relates the distance \( y \) (in miles) and the time \( x \) (in hours) based on the points provided in the graph, we need to find the slope of the line represented by these points.

From the points:

• (1, 15)
• (3, 45)
• (5, 75)

We can observe that for each hour \( x \), the distance \( y \) is given by a consistent ratio.

Let's calculate the slope (which is the constant rate of change) using the point (1, 15):

\[ \text{slope} = \frac{y}{x} = \frac{15}{1} = 15 \]

Now, we can generalize this for any point. The relationship between distance \( y \) and time \( x \) can be expressed as:

\[ y = 15x \]

Thus, the equation relating the distance \( y \) and the time \( x \) is:

\[ y = 15x \]