Question

Derive the equation of the linear relationship represented by the graph showing the cost of renting bicycles, where the horizontal axis is labeled "Number of Bicycles" and ranges from 0 to 6, and the vertical axis is labeled "Cost" and ranges from 0 to 60.

Answer 1

To derive the equation of the linear relationship for the cost of renting bicycles, we can start by analyzing the information provided about the graph.

1. **Identify Key Points**: First, we need to establish two key points from the graph that will help us formulate the equation. Let's assume the following points based on typical scenarios:
- Point A (0 bicycles, $0 cost) - This point indicates that renting 0 bicycles costs $0.
- Point B (6 bicycles, $60 cost) - This point suggests that renting 6 bicycles costs $60.

2. **Determine the Slope (m)**:
The slope of the line can be determined using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For points A and B:
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (6, 60) \)

Substituting these values into the slope formula:
\[
m = \frac{60 - 0}{6 - 0} = \frac{60}{6} = 10
\]

3. **Y-Intercept (b)**:
Since we used the point (0, 0) as one of our points, we know that the y-intercept, \( b \), is 0.

4. **Equation of the Line**:
The general equation for a linear relationship is:
\[
y = mx + b
\]
Substituting \( m = 10 \) and \( b = 0 \) into the equation gives us:
\[
y = 10x
\]

Thus, the equation representing the linear relationship between the cost of renting bicycles (y) and the number of bicycles (x) is:
\[
\text{Cost} = 10 \times \text{Number of Bicycles}
\]

This means that for every bicycle rented, the cost increases by $10.