Question

A line passes through `(8 ,5 )` and `(2 ,1 )`. A second line passes through `(3 ,5 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(0,4)` is a suitable point

Explanation:

Consider the first line passing through the points `(8,5)` and `(2,1)`

The gradient of this line is given by:

`m_1 = (Delta y)/(Delta x) = (5-1)/(8-2) 4/6 = 2/3`

In order for the second line to be parallel to this point it must have the same gradient, So it passes through `(3,5)` and has gradient `2/3`, so we can use the point/gradient formula for a straight line `y-y_1=m(x=x1)` to give;

`y-6=2/3(x-3)`
`y-6=2/3x-2`
`y=2/3x+4`

We can pick any point on this line , choose

`x= 0 => y=4`

Hence `(0,4)` is a suitable point