To find the equation of the linear function that models the relationship between the distance traveled (in miles) and the rental cost (in dollars), we'll use the general form of a linear equation, which is:
\[ f(x) = mx + b \]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept.
Step 1: Identify Two Points from the Graph
From the description, we don't have the exact points, but typically you would find two clear points on the graph. For example, let's assume the graph passes through the points (0, $10) and (25, $30) based on a common scenario for rental car costs.
Step 2: Calculate the Slope (m)
The slope (\( m \)) can be found using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's assume the points are:
- Point 1: (0, 10)
- Point 2: (25, 30)
Using these points:
\[ m = \frac{30 - 10}{25 - 0} = \frac{20}{25} = \frac{4}{5} \]
Step 3: Find the Y-Intercept (b)
The y-intercept (\( b \)) is the value of \( f(x) \) when \( x = 0 \). Based on our assumed first point, \( b = 10 \).
Step 4: Write the Equation
Now that we have both \( m \) and \( b \):
\[ f(x) = \frac{4}{5}x + 10 \]
Final Equation
Thus, the linear function that models the relationship is:
\[ f(x) = \frac{4}{5}x + 10 \]
If you need to enter it in the requested format, it could be:
\[ f(x) = \frac{4}{5}x + 10 \]
Please refer to the graph you're mentioning to verify the points for the correct slope and intercept if needed.