# What is the equation of the line with slope  m= 7/25  that passes through  (41/5 23/10) ?

May 19, 2017

$y = \frac{7}{25} x + \frac{1}{250}$

#### Explanation:

$\text{the equation of a line in "color(blue)"point-slope form}$ 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 $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=7/25" and } \left({x}_{1} , {y}_{1}\right) = \left(\frac{41}{5} , \frac{23}{10}\right)$

$\Rightarrow y - \frac{23}{10} = \frac{7}{25} \left(x - \frac{41}{5}\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{distributing and simplifying gives an alternative equation}$

$y - \frac{23}{10} = \frac{7}{25} x - \frac{287}{125}$

$\Rightarrow y = \frac{7}{25} x - \frac{287}{125} + \frac{23}{10}$

$\Rightarrow y = \frac{7}{25} x + \frac{1}{250} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$