### Video Transcript

The line π΄π΅ is parallel to the
π₯-axis. If the coordinates of the points π΄
and π΅ are seven, negative two and negative seven, π, respectively, find the value
of π.

Any line that is parallel to the
π₯-axis is a horizontal line; this means that youβll have a gradient of zero. The gradient of any line can be
calculated by subtracting the π¦-coordinates, subtracting the π₯-coordinates, and
dividing those two answers.

In this case, we know that the
value of π or the gradient is zero. Substituting in the two coordinates
in this case gives us an equation zero equals negative two minus π divided by seven
minus negative seven. Simplifying the denominator of the
fraction leaves us with 14; seven minus negative seven is plus 14, positive 14. Multiplying both sides of this
equation by 14 leaves this with zero equals negative two minus π. And finally adding π to both sides
of the equation gives us our answer π equals negative two.

Youβll hopefully noticed that the
value of π is equal to the π¦-coordinate of our other points: seven, negative
two. This is because any points that lie
on a line that is parallel to the π₯-axis will have the same π¦-coordinates.

In the diagram, we can see that the
horizontal line parallel to the π₯-axis that passes through negative seven, negative
two and also the point seven, negative two has equation π¦ equals negative two. This is because it crosses the
π¦-axis at the point negative two. This means that all the ordered
pairs or coordinates that lie on the line will have a π¦-coordinate of negative
two.