# How do you find the slope and intercept for x+10y=7?

Jan 8, 2017

Convert to slope-intercept form and pull the correct values from this form of the equation. See the full explanation below.

#### Explanation:

To find the slope and y-intercept we will transform this equation to the slope-intercept form by solving for $y$:

The slope-intercept form of a linear equation is:

$y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and color(blue)(b is the y-intercept value.

$x + 10 y = 7$

$x - \textcolor{g r e e n}{x} + 10 y = - \textcolor{g r e e n}{x} + 7$

$0 + 10 y = - \textcolor{g r e e n}{x} + 7$

$10 y = - \textcolor{g r e e n}{x} + 7$

$\frac{10 y}{\textcolor{g r e e n}{10}} = \frac{- \textcolor{g r e e n}{x} + 7}{\textcolor{g r e e n}{10}}$

$\frac{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{10}}} y}{\cancel{\textcolor{g r e e n}{10}}} = - \frac{1}{10} x + \frac{7}{10}$

$y = \textcolor{red}{- \frac{1}{10}} x + \textcolor{b l u e}{\frac{7}{10}}$

The slope is $m = \textcolor{red}{- \frac{1}{10}}$

The y-intercept is $b = \textcolor{b l u e}{\frac{7}{10}}$