# What is the equation of the line with slope  m= -36/49  that passes through  (26/7, -27/21) ?

Mar 27, 2016

$343 y + 252 x = 495$

#### Explanation:

To find the equation of the line with slope $m = - \frac{36}{49}$ and passing through point $\left(\frac{26}{7} , - \frac{27}{21}\right)$, we use point slope form of equation, which is given by

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$ which, given slope and point $\left({x}_{1} , {y}_{1}\right)$, is

$\left(y - \left(- \frac{27}{21}\right)\right) = \left(- \frac{36}{49}\right) \left(x - \frac{26}{7}\right)$ or

$y + \frac{27}{21} = - \frac{36}{49} x + \frac{36}{49} \times \frac{26}{7}$ or

$y + \frac{27}{21} = - \frac{36}{49} x + \frac{936}{343}$

Now multiplying each term by $343$ , we get

$343 y + \frac{49 \cancel{343} \cdot 9 \cancel{27}}{1 \cancel{21}}$

=$- 7 \cancel{343} \cdot \frac{36}{1 \cancel{49}} x + 1 \cancel{343} \cdot \frac{936}{1 \cancel{343}}$

or $343 y + 441 = - 252 x + 936$ or

$343 y + 252 x = 936 - 441 = 495$