# What is the equation of the line with slope  m= -43/49  that passes through  (19/7, 33/21) ?

Feb 5, 2017

$y = \left(- \frac{43}{49}\right) x + \left(\frac{1356}{343}\right)$

#### Explanation:

To find the equation of a line given the slope and a point of intersection, use the point-slope formula.

The point slope formula is written as: $y - {y}_{1} = m \left(x - {x}_{1}\right)$. Substitute the given information into the formula by setting ${y}_{1} = \frac{33}{21} , {x}_{1} = \frac{19}{7} , \mathmr{and} m = - \frac{43}{49}$.

You should get: $y - \left(\frac{33}{21}\right) = \left(- \frac{43}{49}\right) \left(x - \left(\frac{19}{7}\right)\right)$.

Distribute the slope into $\left(x - \frac{19}{7}\right)$ and get: $y - \left(\frac{33}{21}\right) = \left(- \frac{43}{49}\right) x + \left(\frac{817}{343}\right)$.

Now solve for $y$ by adding $\frac{33}{21}$ to both sides to isolate the variable.

$y = - \frac{43}{49} x + \frac{817}{343} + \frac{33}{21}$

$y = - \frac{43}{49} x + \frac{817}{343} \left(\frac{3}{3}\right) + \frac{33}{21} \left(\frac{49}{49}\right)$

$y = - \frac{43}{49} x + \frac{2451}{1029} + \frac{1617}{1029}$

$y = - \frac{43}{49} x + \frac{4068}{1029}$

$y = - \frac{43}{49} x + \left(\frac{3}{3}\right) \left(\frac{1356}{343}\right)$

You should end up with $y = \left(- \frac{43}{49}\right) x + \left(\frac{1356}{343}\right)$.