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

Mar 30, 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.

Substituting the slope and the values from the point from the problem gives:

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

Solution 1: $\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{2} \left(x + \textcolor{red}{4}\right)$

We can also solve for $y$ to put this equation in slope-intercept form. 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.

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

$y - \textcolor{red}{3} = 2 x + 8$

$y - \textcolor{red}{3} + 3 = 2 x + 8 + 3$

$y - 0 = 2 x + 11$

Solution 2: $y = \textcolor{red}{2} x + \textcolor{b l u e}{11}$