# What is the equation of the line with slope  m= 7/25  that passes through  (14/5 13/10) ?

Feb 9, 2017

$y = \frac{7}{25} x + \frac{129}{250}$

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

$\text{here "m=7/25" and } \left({x}_{1} , {y}_{1}\right) = \left(\frac{14}{5} , \frac{13}{10}\right)$

substitute these values into the equation.

$y - \frac{13}{10} = \frac{7}{25} \left(x - \frac{14}{5}\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

distributing and simplifying gives an alternative version of the equation.

$y - \frac{13}{10} = \frac{7}{25} x - \frac{98}{125}$

$\Rightarrow y = \frac{7}{25} x - \frac{98}{125} + \frac{13}{10}$

$\Rightarrow y = \frac{7}{25} x + \frac{129}{250} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$
graph{7/25x+129/250 [-10, 10, -5, 5]}