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The graph provided in the image shows the relationship between the distance \( D \) (in kilometers) traveled by a boat and the time \( T \) (in hours). The graph appears to be a straight line, indicating a linear relationship between distance and time. 

### Finding the Equation:
For a linear relationship, the equation has the general form:
\[
D = mT + b
\]
where:
- \( D \) is the distance,
- \( T \) is the time,
- \( m \) is the slope (rate of change), and
- \( b \) is the y-intercept.

#### 1. Determine the Slope \( m \):
The slope \( m \) is given by the formula:
\[
m = \frac{\Delta D}{\Delta T} = \frac{\text{change in distance}}{\text{change in time}}
\]

From the graph, we can pick two clear points:
- When \( T = 0 \), \( D = 0 \),
- When \( T = 4 \), \( D = 100 \).

Thus, the slope is:
\[
m = \frac{100 - 0}{4 - 0} = \frac{100}{4} = 25
\]

#### 2. Determine the Y-Intercept \( b \):
From the graph, the line passes through the origin (0, 0), meaning the y-intercept \( b = 0 \).

#### 3. Equation:
Now, substitute the slope and intercept into the equation:
\[
D = 25T
\]

This equation represents the relationship between distance \( D \) and time \( T \).

Would you like further details or clarification on this problem?

### Follow-up Questions:
1. What does the slope of the line represent in real-world terms?
2. How would the equation change if the boat started at a non-zero initial position?
3. What would happen to the graph if the boat's speed doubled?
4. Can you identify another pair of points from the graph to verify the slope?
5. How can you interpret the time when the boat has traveled 200 km using this equation?

### Tip:
Always check the units when determining the slope, as it represents the rate (e.g., kilometers per hour in this case).

A boat is traveling through the water. The graph shows the relationship between the distance D (in kilometers) and the time T (in hours) the boat has traveled. Write an equation to represent the relationship between D and T.

This problem involves determining the linear relationship between distance (D) and time (T) for a boat traveling through water. Using a graph, you will calculate the slope and form a linear equation D = 25T. Suitable for students in Grades 8-10.

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