### Video Transcript

The line π΄π΅ is parallel to the π¦-axis. If the coordinates of the points π΄ and π΅ are π, two and eight, six, respectively, find the value of π.

If two straight lines are parallel, then their slopes or gradients are equal. As π΄π΅ is parallel to the π¦-axis, then the slope of π΄π΅ will be the same as the slope of the π¦-axis. The π¦-axis is a vertical line. This means that the slope is undefined. Therefore, line π΄π΅ will also have a slope that is undefined.

The slope or gradient of any line is calculated using the formula π¦ two minus π¦ one divided by π₯ two minus π₯ one. Substituting in the coordinates of π΄ and π΅ β π, two and eight, six β gives us that the slope is equal to six minus two divided by eight minus π. However, as the slope of π΄π΅ is undefined, the denominator in this case eight minus π must be equal to zero.

Therefore, to work out the value of π, we need to solve the equation eight minus π equals zero. Adding π to both sides of this equation gives us our solution π equals eight. This means that the coordinates of π΄ are eight, two.

We could actually go a step further and say that any point on the line π΄π΅ will have an π₯-coordinate of eight. This is because the equation of the vertical line that passes through eight, two and eight, six is π₯ equals eight.