# Question #171a8

##### 1 Answer
Mar 16, 2017

$y = x + 17 \text{ }$

#### Explanation:

Lines which are parallel have the same slope.
Change the given equation into the form $y = \textcolor{red}{m} x + b$

$4 y - 4 x = 8 \text{ "rarr 4y = 4x +8" } \rightarrow y = \textcolor{red}{1} x + 2$

Now we can see the slope. $\textcolor{red}{m = 1}$

The new line has $\textcolor{red}{m = 1}$ and passes through $\left(\textcolor{b l u e}{- 7} , \textcolor{m a \ge n t a}{10}\right)$

You can use the formula $y - \textcolor{m a \ge n t a}{{y}_{1}} = \textcolor{red}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$y - \left(\textcolor{m a \ge n t a}{10}\right) = \textcolor{red}{1} \left(x - \left(\textcolor{b l u e}{- 7}\right)\right) \text{ } \leftarrow$ now simplify

$y - 10 = x + 7$

$y = x + 7 + 10$

$y = x + 17 \text{ }$ is the equation of the new line.