The slope of the line, calculated as 60, signifies the speed of the train in miles per hour. This interpretation stems from the fundamental understanding that slope represents the rate of change, specifically the change in distance per unit change in time.
(a) **Slope of the Line:**
To find the slope of the line representing the distance traveled by the train over time, we can use the formula for slope, which is the change in distance divided by the change in time. Let's consider two points on the graph, say (1, 60) and (4, 240).
![\[ \text{Slope} = \frac{\text{Change in Distance}}{\text{Change in Time}} = (240 - 60)/(4 - 1) = (180)/(3) = 60 \]](https://img.qammunity.org/2023/formulas/mathematics/college/ry2loykhrzf04oo0pljhcal206bjxfdcxf.png)
So, the slope of the line is 60.
(b) **Meaning of Slope as Rate of Change:**
The slope of the line represents the rate of change of distance with respect to time. In this context, the slope is 60, indicating that for each hour that passes, the train travels an additional 60 miles. This is the speed of the train. Therefore, the train's speed is 60 miles per hour.
In summary, the slope of the line is 60, signifying that the train's speed is 60 miles per hour. This interpretation is derived from the fundamental understanding that slope represents the rate of change, specifically the change in distance per unit change in time.
The question probable may be:
The graph shows the distance a train travels in relation to time. Train Travel Distance (miles) 1 2 3 4 Time (hours) (a) Find the slope of the line. (b) Explain the meaning of the slope as a rate of change. The speed of the train is miles per hour.