Question

A line passes through `(6 ,2 )` and `(1 ,2 )`. A second line passes through `( 7, 4 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(0,4) ; (3,4) ; (-5,4) ; (-7,4)` are all possible points.

Explanation:

Lines which are parallel have the same gradient.
You can find the slope (or gradient) of the first line from the two points that are given.

`m = (y_2-y_1)/(x_2-x_1)`

However, if you look at the points you will see that they have the same `y`-coordinate. This means the line through them is a horizontal line with a slope of `0`

The other line parallel to that one passes through the point `(7,4)`

Any point with a `y`-coordinate of `4` will also like on the line.

`(0,4) ; (3,4) ; (-5,4) ; (-7,4)` are all possible points.