# How do you find the slope of 2x+8y=9?

Dec 11, 2014

In the general form of a line $y = m x + b$, $m$ represents the slope of the line and $b$ the y-intercept. Here, we have the line $2 x + 8 y = 9$...we want it in the form $y = m x + b$ so we can get our $m$ (the slope) directly.

To do this, we simply solve $2 x + 8 y = 9$ for y with some algebra:

$2 x + 8 y = 9$
-Take $2 x$ to the left hand side of the equation by subtracting it from both sides
$8 y = 9 - 2 x = - 2 x + 9$
-Divide by 8 on both sides of the equation to get y alone
$y = - \frac{2}{8} x + \frac{9}{8} = - \frac{1}{4} x + \frac{9}{8}$

And there we have the line $y = - \frac{1}{4} x + \frac{9}{8}$, with $m = s l o p e = - \frac{1}{4}$