# How do you find the equation of the line given m=3, (3,2)?

Feb 19, 2017

$y = 3 x - 7$

#### 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 $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

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

substitute these values into the equation.

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

distributing and simplifying gives an alternative version of the equation.

$y - 2 = 3 x - 9$

$y = 3 x - 9 + 2$

$\Rightarrow y = 3 x - 7 \leftarrow \textcolor{red}{\text{ slope-intercept form}}$