What is the equation of the line with slope  m= 7/25  that passes through  (41/5 -3/10) ?

Dec 24, 2016

$y + \frac{3}{10} = \frac{7}{25} \left(x - \frac{41}{5}\right)$

or

$y = \frac{7}{25} x - \frac{649}{250}$

Explanation:

We can use the slope-point formula to identify the line with the given slope and point.

The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
Where $\textcolor{red}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the information we were provided into this formula gives:

$y - - \frac{3}{10} = \frac{7}{25} \left(x - \frac{41}{5}\right)$

$y + \frac{3}{10} = \frac{7}{25} \left(x - \frac{41}{5}\right)$

If we want to convert to slope-intercept form ($y = m x + b$) we can solve for $y$ as follows:

$y + \frac{3}{10} = \frac{7}{25} x - \left(\frac{7}{25} \times \frac{41}{5}\right)$

$y + \frac{3}{10} = \frac{7}{25} x - \frac{287}{125}$

$y + \frac{3}{10} - \textcolor{red}{\frac{3}{10}} = \frac{7}{25} x - \frac{287}{125} - \textcolor{red}{\frac{3}{10}}$

$y + 0 = \frac{7}{25} x - \frac{287}{125} - \textcolor{red}{\frac{3}{10}}$

$y = \frac{7}{25} x - \frac{287}{125} - \textcolor{red}{\frac{3}{10}}$

$y = \frac{7}{25} x - \left(\frac{287}{125} \times \frac{2}{2}\right) - \left(\textcolor{red}{\frac{3}{10}} \times \frac{25}{25}\right)$

$y = \frac{7}{25} x - \frac{574}{250} - \frac{75}{250}$

$y = \frac{7}{25} x - \frac{649}{250}$