# How do you find the slope given x+9y=18?

Mar 14, 2018

See a solution process below:

#### Explanation:

This equation is in the Standard Linear Form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

$\textcolor{red}{1} x + \textcolor{b l u e}{9} y = \textcolor{g r e e n}{18}$

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Substituting gives a slope of:

$m = - \frac{\textcolor{red}{1}}{\textcolor{b l u e}{9}}$

Mar 14, 2018

$\text{slope } = - \frac{1}{9}$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{rearrange "x+9y=18" into this form}$

$\text{subtract x from both sides}$

$\cancel{x} \cancel{- x} + 9 y = - x + 18$

$\Rightarrow 9 y = - x + 18$

$\text{divide all terms by 9}$

$\frac{\cancel{9} y}{\cancel{9}} = - \frac{1}{9} x + 2$

$\Rightarrow y = - \frac{1}{9} x + 2 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\Rightarrow \text{slope m} = - \frac{1}{9}$