Question

A line passes through `(2 ,4 )` and `(7 ,3 )`. A second line passes through `(8 ,5 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

It is `y=-1/5x+33/5`.

Explanation:

We start calculating the slope of the line passing by the first two points.

The generic question is
`y=mx+q`
substituting the points we have
`4=2m+q`
`3=7m+q`
From the first equation I have
`q=4-2m`
I substitute this value in the second equation
`3=7m+4-2m` then
`-1=5m` and
`m=-1/5`.

Now we know that all the lines with the same slope are parallels.
So the line passing by the third point has equation

`y=-1/5m+q` and we have to find the `q` imposing the passage from `(8,5)`.

`5=-1/5*8+q`

`q=5+8/5=33/5`

Then the equation of the desired line is

`y=-1/5x+33/5`.