# How do you write an equation of a line with point (2,6), slope 2?

Jan 18, 2017

See the entire solution process below:

#### Explanation:

To write this equation we can use the point-slope formula.

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 values from the problem gives this equation:

$\left(y - \textcolor{red}{6}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{2}\right)$

We can also solve for $y$ to put this equation into the more familiar 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.

$y - \textcolor{red}{6} = \left(\textcolor{b l u e}{2} \times x\right) - \left(\textcolor{b l u e}{2} \times \textcolor{red}{2}\right)$

$y - \textcolor{red}{6} = 2 x - 4$

$y - \textcolor{red}{6} + 6 = 2 x - 4 + 6$

$y - 0 = 2 x + 2$

$y = 2 x + 2$