Question

A line passes through `(2 ,9 )` and `(5 ,2 )`. A second line passes through `(3 ,8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

Answer: `(0, 15)`

Explanation:

First, find the slope of the first line by using

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

In this case, you have

`m = (2 - 9)/(5 -2)= -7/3`

Now with the slope of `-7/3`, we have to find two coordinates with the exact same slope. So we put it in the slope formula

`(8- ?)/(3 - ?) = -7/3`

which is the slope we have to find. We could use `15` and `0`, and when we input them back into the equation the slope equals `-7/3`.

But since the slope formula is `m = (y_2 - y_1) / (x_2 - x_1)`, we often get confused and say `(15,0)` and forget it's `y` over `x`. So remember to switch them so `x=0` and `y=15`.

To continue, if something is parallel to another line they have the same slope.

If something is perpendicular it has the opposite reciprocal slope.