A mail delivery person delivers mail to 20 houses every 15 minutes at a constant rate. He graphs the linear relationship on a coordinate grid, where the \( x \)-axis represents the number of minutes and the \( y \)-axis represents the number of houses. What is the slope of the linear relationship? When

To determine the slope of the linear relationship between the number of minutes (\( x \)) and the number of houses (\( y \)) delivered, we can use the given information: - **Rate of Delivery:** 20 houses every 15 minutes. The slope (\( m \)) of a linear equation \( y = mx + b \) represents the rate of change of \( y \) with respect to \( x \). In this context, it signifies how many houses are delivered per minute. **Calculating the Slope:** \[ m = \frac{\Delta y}{\Delta x} = \frac{20 \text{ houses}}{15 \text{ minutes}} = \frac{4}{3} \text{ houses per minute} \] **Conclusion:** The slope of the linear relationship is \( \frac{4}{3} \) houses per minute. This means that, on average, the mail delivery person delivers \( \frac{4}{3} \) houses every minute. **Answer:** Since he delivers 20 houses in 15 minutes, the slope is 20⁄15 = 4⁄3 houses per minute.