# How do you show that if a+b=0, then the slope of x/a+y/b+c=0 is 1?

Dec 19, 2015

Solve the linear equation for $y$ to obtain the slope-intercept form, and use the conditions on $a$ and $b$ to show that the slope is $1$.

#### Explanation:

If we solve a linear equation for $y$ we get the slope-intercept form $y = m x + b$ where $m$ is the slope of the graph and $b$ is the
$y$-intercept.

Doing so in the given case, we have

$\frac{x}{a} + \frac{y}{b} + c = 0$

$\implies \frac{y}{b} = - \frac{1}{a} x - c$

$\implies y = - \frac{b}{a} x - c$

Thus the slope $m$ is $\frac{- b}{a}$

But from $a + b = 0$ we can subtract $b$ from both sides to obtain $a = - b$. Substituting this into the above slope, we get

$m = \frac{- b}{a} = \frac{- b}{- b} = 1$