# How do you write an equation of a line with point (2,-2), slope 2/7?

Jan 26, 2017

$y = \frac{2}{7} x - \frac{18}{7}$

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

$\text{here "m=2/7" and } \left({x}_{1} , {y}_{1}\right) = \left(2 , - 2\right)$

substituting these values into the equation.

$y - \left(- 2\right) = \frac{2}{7} \left(x - 2\right)$

$\Rightarrow y + 2 = \frac{2}{7} \left(x - 2\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

distributing the bracket and simplifying gives an alternative version of the equation.

$y + 2 = \frac{2}{7} x - \frac{4}{7}$

$\Rightarrow y = \frac{2}{7} x - \frac{18}{7} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$