# How do you find the equation of the line with slope m=7/8 and point (1,-2)?

Jan 3, 2017

$y = \frac{7}{8} x - \frac{23}{8}$

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

$\text{here " m=7/8" and } \left({x}_{1} , {y}_{1}\right) = \left(1 , - 2\right)$

substitute these values into the equation.

$y + 2 = \frac{7}{8} \left(x - 1\right) \leftarrow \text{ in point-slope form}$

If we distribute and simplify we obtain an alternative form of the equation.

$y + 2 = \frac{7}{8} x - \frac{7}{8}$

$\Rightarrow y = \frac{7}{8} x - \frac{7}{8} - 2$

$\Rightarrow y = \frac{7}{8} x - \frac{23}{8} \leftarrow \text{ in slope-intercept form}$