How do you find the Slope, Y-intercept and X-intercept of the Line x-3y+7=0?

Jan 14, 2017

See the entire process for answering these questions below:

Explanation:

First, to find the slope and y-intercept we can convert this equation into 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.

$x - 3 y + 7 + \textcolor{red}{3 y} = 0 + \textcolor{red}{3 y}$

$x - 3 y + \textcolor{red}{3 y} + 7 = \textcolor{red}{3 y}$

$x - 0 + 7 = \textcolor{red}{3 y}$

$x + 7 = 3 y$

or

$3 y = x + 7$

$\frac{3 y}{\textcolor{red}{3}} = \frac{x + 7}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} y}{\cancel{\textcolor{red}{3}}} = \frac{x}{3} + \frac{7}{3}$

$y = \frac{1}{3} x + \frac{7}{3}$

Therefore:

The slope is $\textcolor{red}{m = \frac{1}{3}}$

The y-intercept is $\textcolor{b l u e}{b = \frac{7}{3}}$ or (0, 7/3)

To find the x-intercept we set $y = 0$ and solve for $x$:

$0 = \frac{1}{3} x + \frac{7}{3}$

$0 - \textcolor{red}{\frac{7}{3}} = \frac{1}{3} x + \frac{7}{3} - \textcolor{red}{\frac{7}{3}}$

$- \frac{7}{3} = \frac{1}{3} x + 0$

$- \frac{7}{3} = \frac{1}{3} x$

$\textcolor{red}{3} \times - \frac{7}{3} = \textcolor{red}{3} \times \frac{1}{3} x$

$\cancel{\textcolor{red}{3}} \times - \frac{7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \cancel{\textcolor{red}{3}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} x$

$- 7 = x$ or $x = - 7$

Therefore:

The x-intercept is $\textcolor{g r e e n}{x = - 7}$ or (-7, 0)