# Question #89b0d

Jun 23, 2017

$y = - \frac{8}{9} x + \frac{1}{9}$

#### Explanation:

Slope-intercept form is $y = m x + b$.

So how do we write $8 x + 9 y = 1$ in this form? Well, we need to isolate $y$ on one side and get everything else on the other side!

1. Our first step is to subtract $8 x$ from both sides, so that only $9 y$ remains on the left side.

$8 x + 9 y = 1$
$\cancel{8 x} + 9 y \cancel{\textcolor{red}{- 8 x}} = 1 \textcolor{red}{- 8 x}$
$9 y = 1 - 8 x$

We can switch the order of the $1$ and the $- 8 x$, because of the commutative property. So now we have

$9 y = - 8 x + 1$

2. Divide both sides by $9$ to get only $y$ on the left side.

$\frac{9 y}{9} = \frac{- 8 x}{9} + \frac{1}{9}$

$y = - \frac{8}{9} x + \frac{1}{9}$

Now the equation is in slope-intercept form!

The slope (m) is $- \frac{8}{9}$ and the y-intercept (b) is $\frac{1}{9}$.