# What is the slope intercept form of the line passing through (3,-20)  with a slope of -1/2 ?

Jul 31, 2017

See a 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 from the problem for $m$ and the values from the point in the for $x$ and $y$. We can than solve the equation for $\textcolor{b l u e}{b}$.

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

$- 20 = \left(\textcolor{red}{- \frac{1}{2}} \times 3\right) + \textcolor{b l u e}{b}$

$- 20 = - \frac{3}{2} + \textcolor{b l u e}{b}$

$\textcolor{red}{\frac{3}{2}} - 20 = \textcolor{red}{\frac{3}{2}} - \frac{3}{2} + \textcolor{b l u e}{b}$

$\textcolor{red}{\frac{3}{2}} - \left(\frac{2}{2} \times 20\right) = 0 + \textcolor{b l u e}{b}$

$\textcolor{red}{\frac{3}{2}} - \frac{40}{2} = \textcolor{b l u e}{b}$

$- \frac{37}{2} = \textcolor{b l u e}{b}$

Substituting the slope from the problem and the value for $\textcolor{b l u e}{b}$ we calculated into the formula gives:

$y = \textcolor{red}{- \frac{1}{2}} x + \textcolor{b l u e}{- \frac{37}{2}}$

$y = \textcolor{red}{- \frac{1}{2}} x - \textcolor{b l u e}{\frac{37}{2}}$