# Math Help - find x if the slope of the line...

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

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

2. Let $m_1$ be the slope of the first line, and $m_2$ 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 :

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

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

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

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

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

Solve the last equation for $x$.

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