# How do you write an equation of a line given (-4,2), m=3/2?

Apr 7, 2017

Use the equation $y = m x + b$

the slope or $m$ is already given therfore the equation now looks like,

$y = \frac{3}{2} x + b$

Solve for $b$ by subbing point $P \left(- 4 , 2\right)$

$2 = \frac{3}{2} \cdot \left(- 4\right) + b$

$2 = - 6 + b$

$b = 8$

Therefore the equation of the line is,

$y = \frac{3}{2} x + 8$

graph{3/2x+8 [-10, 10, -5, 5]}

Apr 7, 2017

See the entire solution process below:

#### Explanation:

We can use the point-slope formula to write an equation for this line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substitute the slope and point from the problem gives:

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{\frac{3}{2}} \left(x - \textcolor{red}{- 4}\right)$

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{\frac{3}{2}} \left(x + \textcolor{red}{4}\right)$

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

$y - \textcolor{red}{2} = \left(\textcolor{b l u e}{\frac{3}{2}} \times x\right) + \left(\textcolor{b l u e}{\frac{3}{2}} \times \textcolor{red}{4}\right)$

$y - \textcolor{red}{2} = \frac{3}{2} x + \frac{12}{2}$

$y - \textcolor{red}{2} = \frac{3}{2} x + 6$

$y - \textcolor{red}{2} + 2 = \frac{3}{2} x + 6 + 2$

$y - 0 = \frac{3}{2} x + 8$

$y = \textcolor{red}{\frac{3}{2}} x + \textcolor{b l u e}{8}$