# What is the equation of the line with slope  m= 8/25  that passes through  (41/5 21/10) ?

Feb 5, 2017

(y - color(red)(21/10)) = color(blue)(8/25)(x - color(red)(41/5))#

Or

$y = \frac{8}{25} x - \frac{131}{250}$

#### Explanation:

We can use the point-slope formula to write an equation of the line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the information from the problem gives:

$\left(y - \textcolor{red}{\frac{21}{10}}\right) = \textcolor{b l u e}{\frac{8}{25}} \left(x - \textcolor{red}{\frac{41}{5}}\right)$

We can solve for $y$ to convert to the more familiar slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$y - \textcolor{red}{\frac{21}{10}} = \left(\textcolor{b l u e}{\frac{8}{25}} \times x\right) - \left(\textcolor{b l u e}{\frac{8}{25}} \times \textcolor{red}{\frac{41}{5}}\right)$

$y - \textcolor{red}{\frac{21}{10}} = \frac{8}{25} x - \frac{328}{125}$

$y - \textcolor{red}{\frac{21}{10}} + \frac{21}{10} = \frac{8}{25} x - \frac{328}{125} + \frac{21}{10}$

$y - 0 = \frac{8}{25} x - \left(\frac{2}{2} \times \frac{328}{125}\right) + \left(\frac{25}{25} \times \frac{21}{10}\right)$

$y = \frac{8}{25} x - \frac{656}{250} + \frac{525}{250}$

$y = \frac{8}{25} x - \frac{131}{250}$