What is the equation of the line passing through (2, –3) and parallel to the line y = –6x – 1 in standard form?

May 18, 2015

The answer is $6 x + y - 9 = 0$

You start by noting that the function you are looking for can be written as $y = - 6 x + c$ where $c \in \mathbb{R}$ because two parallel lines have the same "x" coeficients.
Next you have to calculate $c$ using the fact that the line passes through $\left(2 , - 3\right)$
After solving the equation $- 3 = - 6 \cdot 2 + c$
$- 3 = - 12 + c$
$c = 9$
So the line has the equation $y = - 6 x + 9$
To change it to the standard form you just have to move $- 6 x + 9$ to the left side to leave $0$ on the right side, so you finally get:
$6 x + y - 9 = 0$