# How do you find the equation in slope - intercept form, of the line passing through: (-1,-1) slope = 4?

Mar 19, 2017

See the entire solution process below:

#### Explanation:

First, using the information in the problem write the equation in point-slope form. 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 information from the problem gives:

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

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

Now, we solve for $y$ to transform the equation to 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.

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

$y + \textcolor{red}{1} = \left(\textcolor{b l u e}{4} \times x\right) + \left(\textcolor{b l u e}{4} \times \textcolor{red}{1}\right)$

$y + \textcolor{red}{1} = 4 x + 4$

$y + \textcolor{red}{1} - 1 = 4 x + 4 - 1$

$y + 0 = 4 x + 3$

$y = \textcolor{red}{4} x + \textcolor{b l u e}{3}$