# What is the slope intercept form of the line passing through (-10,6)  with a slope of 3/2 ?

Aug 28, 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 to give:

$y = \textcolor{red}{\frac{3}{2}} x + \textcolor{b l u e}{b}$

Into the equation we can now substitute the values from the point for $x$ and $y$ and then solve for $\textcolor{b l u e}{b}$

$6 = \left(\textcolor{red}{\frac{3}{2}} \times - 10\right) + \textcolor{b l u e}{b}$

$6 = - \textcolor{red}{\frac{30}{2}} + \textcolor{b l u e}{b}$

$6 = - \textcolor{red}{15} + \textcolor{b l u e}{b}$

$15 + 6 = 15 - \textcolor{red}{15} + \textcolor{b l u e}{b}$

$21 = 0 + \textcolor{b l u e}{b}$

$21 = \textcolor{b l u e}{b}$

We can now substitute this along with the into the formula to give:

$y = \textcolor{red}{\frac{3}{2}} x + \textcolor{b l u e}{21}$