### 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 ๐ฆ equals ๐๐ฅ plus ๐,
where ๐ is the slope or gradient of the line. The value of ๐ can be
calculated using the formula ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one. This is the change in
๐ฆ-coordinates over the change in ๐ฅ-coordinates, otherwise known as the rise
over the run. We begin by selecting any two
points on the line ๐ด and ๐ต with coordinates ๐ฅ one, ๐ฆ one and ๐ฅ two, ๐ฆ
two. Whilst it doesnโt 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 ๐ด has coordinates zero,
one and point ๐ต 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 ๐ฆ-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 ๐ฆ-coordinates were
seven and one. And the corresponding
๐ฅ-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.