Video: Calculating the Slope of a Line in a Graph

Calculate the slope of the line in the graph.


Video Transcript

Calculate the slope of the line in the graph.

We know that any straight line is a linear function that can be written in the form ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘, where ๐‘š is the slope or gradient of the line. The value of ๐‘š can be calculated using the formula ๐‘ฆ two minus ๐‘ฆ one over ๐‘ฅ two minus ๐‘ฅ one. This is the change in ๐‘ฆ-coordinates over the change in ๐‘ฅ-coordinates, otherwise known as the rise over the run. We begin by selecting any two points on the line ๐ด and ๐ต with coordinates ๐‘ฅ one, ๐‘ฆ one and ๐‘ฅ two, ๐‘ฆ two. Whilst it doesnโ€™t matter which two points we choose, it is sensible to pick those with integer coordinates where possible.

In this question, we will choose the two points shown on the graph. Point ๐ด has coordinates zero, one and point ๐ต has coordinates two, seven. At this point, it is worth drawing a right-angled triangle on the graph to show the rise and the run. The rise in this case is equal to six, as the change in ๐‘ฆ-coordinates is six. The run is equal to two. This means that we would expect the slope to be six divided by two, which is three.

We can check this by substituting our coordinates into the formula. The two ๐‘ฆ-coordinates were seven and one. And the corresponding ๐‘ฅ-coordinates were two and zero. This simplifies to six over two, which once again gives us an answer of three. The slope of the line in the graph is three. It is worth recalling that any line that slopes upwards from left to right will have a positive slope. As three is positive, this suggests that our answer is correct.

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