Question

A line passes through `(2 ,8 )` and `(3 ,9 )`. A second line passes through `(7 ,6 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

See the explanantion

Explanation:

`color(blue)("Consider line 1")`

Gradient is the amount of up/down for the amount of along when reading left to right.

The amount of along is the change in the x-axis`->3-2=+1`
The amount of up/down is the change in y-axis`->9-8=+1`

The gradient `->(y_2-y_1)/(x_2=x_1) = 1/1 =1`

That is, the amount of change for the x-axis is the same as the amount of change for the y-axis
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider line 2")`

Thus for line 2 I chose a change of +3.

So if the first point is `(7,6)` then the second one I chose would be

`(7+3,6+3) = (10,9)`