Question

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

Answer 1

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

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