# Thread: find x if the slope of the line...

1. ## find x if the slope of the line...

find $\displaystyle x$ if the slope of the line through $\displaystyle (1,2)$ and $\displaystyle (x,0)$ is the negative of the slope of the
line through $\displaystyle (4,5)$ and $\displaystyle (x,0)$
I know that these slopes do not have to be perpendicular to each other.

2. Let $\displaystyle m_1$ be the slope of the first line, and $\displaystyle m_2$ be the slope of the second line ..

Since the slope of the first line is the negative of the slope of the second line, we conclude that :

$\displaystyle m_1=-m_2$ ..... (1)

$\displaystyle m_1=\frac{0-2}{x-1}=\frac{-2}{x-1}$ ... (2)

$\displaystyle m_2=\frac{0-5}{x-4}=\frac{-5}{x-4}$ ... (3)

If we substitute (2) & (3) in (1), we will get the following equation :

$\displaystyle \frac{-2}{x-1}=\frac{5}{x-4}$

Solve the last equation for $\displaystyle x$.

3. you have to solve:
-2/(x-1)=5/(x-4)
if x<>1 and x<>4 then this is equivalent to -2(x-4)=5(x-1)
7x=13