# How do you write an equation of a line going through (1/8, −1) and parallel to the line 8x − 9y = 6?

Aug 15, 2017

$y = \frac{8}{9} x - 1 \frac{1}{9}$

#### Explanation:

Parallel lines have the same slope. So we can find the required slope from the equation of the given line.
Change it into the form $y = \textcolor{b l u e}{m} x + c$

$9 y = 8 x - 6$

$y = \textcolor{b l u e}{\frac{8}{9}} x - \frac{2}{3} \text{ } \rightarrow$ this gives us $\textcolor{b l u e}{m = \frac{8}{9}}$

You can use the formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$ because we have a point $\left(\frac{1}{8} , - 1\right)$ and the slope $\textcolor{b l u e}{m = \frac{8}{9}}$

$y - {y}_{1} = \textcolor{b l u e}{m} \left(x - {x}_{1}\right)$

$y - \left(- 1\right) = \textcolor{b l u e}{\frac{8}{9}} \left(x - \frac{1}{8}\right)$

$y + 1 = \frac{8}{9} x - \frac{1}{9} \text{ } \leftarrow \left[\frac{\cancel{8}}{9} \times \frac{1}{\cancel{8}} = \frac{1}{9}\right]$

$y = \frac{8}{9} x - 1 \frac{1}{9} \text{ } \leftarrow \left[- 1 - \frac{1}{9} = - 1 \frac{1}{9}\right]$

As we expected, the slope of the new line is $\frac{8}{9}$