# How do you write an equation of a line with point (3,1), slope 2?

Feb 14, 2017

$y = 2 x - 5$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here "m=2" and } \left({x}_{1} , {y}_{1}\right) = \left(3 , 1\right)$

$\Rightarrow y - 1 = 2 \left(x - 3\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

distributing and simplifying gives an alternative version.

$y - 1 = 2 x - 6$

$\Rightarrow y = 2 x - 6 + 1$

$\Rightarrow y = 2 x - 5 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$