A line passes through (2 ,8 ) and (4 ,9 ). 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?

Jan 3, 2017

$\left(1 , 4\right)$

Explanation:

If you want two lines to be parallel, then the slopes have to be identical.

What is a slope, you may ask?

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

So now let's find the slope of the first two coordinates listed, $\left(2 , 8\right)$ and $\left(4 , 9\right)$.

Input them into the equation

$m = \frac{9 - 8}{4 - 2} = \frac{1}{2}$

So, the slope is 1/2. Now we only know one of the coordinates to find the answer, so we will input one of the coordinates but put the unknown numbers as "?". For $\left(3 , 5\right)$, you have

(5 - ?)/(3 - ?) = 1/2

Now we see that $4$ could be a logical number for $y$ and $1$ could be a logical number for $x$. But let's double check.

$\frac{5 - 4}{3 - 1} = \frac{1}{2}$

Therefore, the coordinates are $\left(1 , 4\right)$.

Be sure to remember that if two lines are parallel then their slopes are the same and if two lines are perpendicular their slopes are opposite reciprocal.

For example, if the slope is $7$ and you want to make it perpendicular it would be $- \frac{1}{7}$. Another example would be if the slope was $- \frac{1}{2}$ and you want to make it perpendicular then the slope would be $2$.

Good luck!