Question Video: Finding the Slope of a Straight Line Mathematics

The given table shows the relation between the distance covered by a runner and a certain time. Determine the slope of the straight line that represents the motion of the runner.

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Video Transcript

The given table shows the relation between the distance covered by a runner and a certain time. Determine the slope of the straight line that represents the motion of the runner.

There are two ways of approaching this problem. The first way would be to draw a distance–time graph from the information in the table. On the 𝑥-axis, we have the time in seconds and on the 𝑦-axis the distance in meters. We can then plot the six points zero, zero; two, eight; four, 16; and so on, as shown on the graph. We can then calculate the slope or gradient of the straight line by dividing the change in the 𝑦-coordinate by the change in the 𝑥-coordinate.

If we choose the two endpoints of the graph, we see that the change in 𝑦 is equal to 40 and the change in 𝑥 is equal to 10. The slope is therefore equal to 40 divided by 10. This is equal to four. We know that the slope on a distance–time graph represents speed. As the distance is in meters and the time is in seconds, the slope or speed will be equal to four meters per second.

An alternate method in this question without drawing a diagram would be to recognize that the slope will be equal to the change in distance divided by the change in time. We could then select any two points from the table, for example, a time of two seconds and distance of eight meters and a time of eight seconds and distance of 32 meters. The change in distance here is equal to 32 minus eight. The change in time is equal to eight minus two. This simplifies to 24 divided by six, which once again is equal to four meters per second.

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