Question

A line passes through `(1 ,5 )` and `(8 ,7 )`. A second line passes through `(3 ,6 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(10,8)`

Explanation:

I didn't use math to figure this out, but I'll explain both ways. First the easy way.

To get from `(1,5)` to `(3,6)`, you increase `x` by `2` and `y` by `1`, so if you do the same thing to `(8,7)`, you get `(10,8)`. If you move both points by the same amount, the slope stays the same.

Mathematically, you would have to find the slope of the line made by `(1,5)` and `(8,7)`. So you do the slope formula, and you get

`"slope" = m = (7-5)/(8-1`

which equals `2/9`. Then you use the point-slope formula and input `(3,6)` for the `x` and `y` variables and `2/9` for the `m` variable.

You end up with

`y-6=(2/7)(x-3)`

which, when you solve for `y`, becomes

`y=2/7x+36/7`

(I kept the fractions so it would be easier to solve).

Then just pick an `x` value and plug it in yo get your `y` and you're done. Yay! (You'll notice that plugging in `10` gets you `56/7`, which is `8`)