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?

Jan 2, 2017

Answer: $\left(0 , 15\right)$

Explanation:

First, find the slope of the first line by using

$\text{slope} = m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

In this case, you have

$m = \frac{2 - 9}{5 - 2} = - \frac{7}{3}$

Now with the slope of $- \frac{7}{3}$, 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 $- \frac{7}{3}$.

But since the slope formula is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, we often get confused and say $\left(15 , 0\right)$ 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.