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Let's analyze the problem step by step.

The problem states that the distance \( d \) you bike varies directly with the time \( t \) spent biking. The problem gives that you bike **9.8 miles in 1.25 hours**. You are asked to find the equation that relates \( d \) and \( t \), and then choose the correct graph.

### Step 1: Find the equation
Since the distance varies directly with time, the relationship between \( d \) and \( t \) can be written as:

\[
d = k \cdot t
\]

where \( k \) is the constant of proportionality (rate of biking, in miles per hour). To find \( k \), use the given information:
\[
d = 9.8 \, \text{miles}, \quad t = 1.25 \, \text{hours}
\]
Substitute into the equation to solve for \( k \):

\[
9.8 = k \cdot 1.25
\]
\[
k = \frac{9.8}{1.25} = 7.84
\]

Thus, the equation relating \( d \) and \( t \) is:
\[
d = 7.84t
\]

This matches option **B**.

### Step 2: Graph the equation
Now that we have the equation \( d = 7.84t \), we know that it is a linear equation with a slope of 7.84 and a y-intercept of 0 (since there is no constant term added to \( d \)).

To choose the correct graph:
- The slope of 7.84 means the line should be steep.
- It should pass through the origin (0, 0).
- It should go through the point \( (1.25, 9.8) \), since that was given in the problem.

Looking at the graphs:
- The graph in **B** shows a steep line with a correct steepness, passing through the point \( (1.25, 9.8) \). Therefore, **B** is the correct graph.

### Final Answer:
The correct equation is **B** \( d = 7.84t \), and the correct graph is also **B**.

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Would you like more details on any part of the solution?

Here are 5 related questions to expand on this problem:

1. How would the graph change if the biking speed increased?
2. What does the slope of the line represent in the context of this problem?
3. How would you interpret the y-intercept in this scenario, and what does it mean practically?
4. How would you use this equation to calculate the distance biked in 2 hours?
5. Can this equation be applied to find the time required to bike a certain distance? How?

**Tip:** When working with direct variation problems, always remember that the constant of proportionality represents the rate of change (in this case, the speed or biking rate).

The distance d you bike varies directly with the amount of time t you bike. Suppose you bike 9.8 mi in 1.25 h. What is an equation that relates d and t? What is the graph of the equation?

Learn how to solve a direct variation problem where distance varies with time. This problem shows how to find the biking rate and graph the equation. Perfect for students in Grades 6-8 studying proportionality and linear equations.

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