# What is the slope intercept form of the line passing through (-4,7)  with a slope of -1/3 ?

Apr 23, 2017

See the entire solution process below:

#### Explanation:

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 $\textcolor{b l u e}{b}$ is the y-intercept value.

We can substitute the slope and values for the point from the problem for $m$, $x$ and $y$ in the formula and solve for $b$:

$7 = \left(\textcolor{red}{- \frac{1}{3}} \cdot - 4\right) + \textcolor{b l u e}{b}$

$7 = \frac{4}{3} + \textcolor{b l u e}{b}$

$7 - \textcolor{red}{\frac{4}{3}} = \frac{4}{3} - \textcolor{red}{\frac{4}{3}} + \textcolor{b l u e}{b}$

$\left(\frac{3}{3} \cdot 7\right) - \textcolor{red}{\frac{4}{3}} = 0 + \textcolor{b l u e}{b}$

$\frac{21}{3} - \textcolor{red}{\frac{4}{3}} = \textcolor{b l u e}{b}$

$\frac{17}{3} = \textcolor{b l u e}{b}$

We can now substitute the slope given in the problem and the value for $b$ we calculated into the slope-intercept formula to find the equation to solve the problem:

$y = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{\frac{17}{3}}$