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**Slope as Rate of Change

Distance (miles)
180
160
140
120
100
80
60
40
Time (hours)
A m = 80
4x What is the slope (m) of the line shown on the
graph?
4x B m = 60
4x C m = 40
4x D
m = 20
5 of 10
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The distanco in
x Which statement is appropriate when interpreting the
slope of the given line as a rate of change? Answer or I will sue

User Dlaor
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1 Answer

4 votes

Final answer:

The slope of a line, representing rate of change, is calculated by dividing the change in distance by the change in time between two points on the line. Without a graph to refer to, we can't select the correct option; however, the method to find slope remains the same regardless of specific values.

Step-by-step explanation:

To find the slope of a line, also known as the rate of change, you need to select any two points on the line. In a graph representing distance over time, the slope can be calculated using the formula:

Slope (m) = (Change in distance) / (Change in time) = Δdistance / Δtime

For instance, if the graph shows two points at (2 hours, 160 miles) and (5 hours, 100 miles), the slope would be calculated as:

m = (100 miles - 160 miles) / (5 hours - 2 hours)

m = (-60 miles) / (3 hours) = -20 miles per hour

This means the slope of the line, or the rate of change of distance with respect to time, is -20 miles per hour, meaning the distance decreases by 20 miles every hour. The negative sign indicates the distance is decreasing over time.

In the context provided by the question, without a graph to refer to, we can't specify which of the provided options (A, B, C, D) is correct. However, the correct slope value would be represented by the difference in distance divided by the difference in time between two points on the graph.

User Bryant
by
8.1k points

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