# What is the equation of the line with slope  m= -3/49  that passes through  (17/7,14/7) ?

Mar 5, 2017

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{- \frac{3}{49}} \left(x - \textcolor{red}{\frac{17}{7}}\right)$

Or

$y = \textcolor{red}{- \frac{3}{49}} x + \textcolor{b l u e}{\frac{737}{343}}$

#### Explanation:

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 slope and point from the problem gives:

$\left(y - \textcolor{red}{\frac{14}{7}}\right) = \textcolor{b l u e}{- \frac{3}{49}} \left(x - \textcolor{red}{\frac{17}{7}}\right)$

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{- \frac{3}{49}} \left(x - \textcolor{red}{\frac{17}{7}}\right)$

We can convert this formula to the slope-intercept form by solving for $y$. 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.

$y - \textcolor{red}{2} = \left(\textcolor{b l u e}{- \frac{3}{49}} \times x\right) - \left(\textcolor{b l u e}{- \frac{3}{49}} \times \textcolor{red}{\frac{17}{7}}\right)$

$y - \textcolor{red}{2} = - \frac{3}{49} x - \left(- \frac{51}{343}\right)$

$y - \textcolor{red}{2} = - \frac{3}{49} x + \frac{51}{343}$

$y - \textcolor{red}{2} + 2 = - \frac{3}{49} x + \frac{51}{343} + 2$

$y - 0 = - \frac{3}{49} x + \frac{51}{343} + \left(2 \times \frac{343}{343}\right)$

$y = - \frac{3}{49} x + \frac{51}{343} + \frac{686}{343}$

$y = \textcolor{red}{- \frac{3}{49}} x + \textcolor{b l u e}{\frac{737}{343}}$