# Consider the line y=8x-2. What is the equation of the line that is parallel to this line and passes through the point (-5,6)?

Nov 26, 2015

$y = 8 x + 46$

#### Explanation:

All lines with the same slope are parallel to each other.

All lines with a slope $8$ have equation
$y = 8 x + C$
where $C$ is some constant.

Let's find a constant $C$ such that point $\left(- 5 , 6\right)$ lies on a line:
$6 = 8 \left(- 5\right) + C$
from which follows:
$C = 46$

Therefore, line $y = 8 x + 46$ is parallel to a given line $y = 8 x - 2$ and passes through point $\left(- 5 , 6\right)$.