# How do you write an equation of a line with slope = 2 and contains point (-1 , 4)?

Apr 17, 2017

$y = 2 x + 6$

#### Explanation:

The general format for the point-intercept quation is $y = m x + b$

Where $m =$slope and $b =$y-intercept

Given the slope is $2$, the equation now looks like $y = 2 x + b$

Given $P \left(- 1 , 4\right)$ we can solve for the $b$ variable by substituting the $x$ and $y$ cordinates.

$4 = 2 \cdot \left(- 1\right) + b$
$4 = - 2 + b$
$b = 6$

Therefore the equation that has the slope of $2$ and passes through the point $\left(- 1 , 4\right)$ is $y = 2 x + 6$

Here's a graphical look,

graph{2x+6 [-10, 10, -5, 10]}

Apr 17, 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 values from the point in the problem gives:

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

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

We can solve this equation for $y$ to put the 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.

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

$y - \textcolor{red}{4} = 2 x + 2$

$y - \textcolor{red}{4} + 4 = 2 x + 2 + 4$

$y - 0 = 2 x + 6$

$y = \textcolor{red}{2} x + \textcolor{b l u e}{6}$