# What is the equation of the line with slope  m= 8/49  that passes through  (2/7, 1/21) ?

May 27, 2018

color(indigo)(168x - 1029y + 1 = 0

#### Explanation:

Point-Slope equation form is

$\left(y - {y}_{1}\right) = m \cdot \left(x - {x}_{1}\right)$

$y - \left(\frac{1}{21}\right) = \left(\frac{8}{49}\right) \cdot \left(x - \left(\frac{2}{7}\right)\right)$

$\frac{21 y - 1}{\cancel{21}} ^ \textcolor{red}{3} = \frac{56 x - 16}{49 \cdot \cancel{7}}$

$\left(21 y - 1\right) \cdot 49 = 3 \cdot \left(56 x - 16\right)$

$1029 y - 49 = 168 x - 48$

color(indigo)(168x - 1029y + 1 = 0

May 27, 2018

Shown below...

#### Explanation:

If you are unfamiliar with $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Use $y = m x + c$

$\implies y = \frac{8}{49} x + c$

Now find $c$ by subbing in $x = \frac{2}{7}$ and $y = \frac{1}{21}$

$\implies \frac{1}{21} = \left(\frac{8}{49} \cdot \frac{2}{7}\right) + c$

$\implies \frac{1}{21} = \frac{16}{343} + c$

$\implies c = \frac{1}{21} - \frac{16}{343}$

$\implies c = \frac{1}{1029}$

$\implies y = \frac{8}{49} x + \frac{1}{1029}$

Both solutions are valid for this