Question

what is a equation of the line that passes through the point (-4,-6) and is parallel to the line 3x-y=6

Answer 1

`y=3x+6`

Explanation:

When solving these types of problems you need to know how to write a line that is parallel to another line. Parallel lines have the same SLOPE but different y-intercepts. But in order to do this, we need to convert this equation to slope-intercept form: y=mx+b.

First, we want to get -y by itself therefore we want to subtract 3x on both sides to get
`-y=-3x+6`. We then want to isolate y by dividing by -1 on each side to get the new equation
`y=3x-6`. We can then use this equation to make a line that is parallel.

Utilizing the slope from the original equation (3) and using the same format for slope-intercept, we get
`y=3x+b`. Our line goes through a certain point therefore our x and y values are given so that our equation looks like
`-6=3(-4)+b`. We now simplify to get
`-6=-12+b` and add 12 on both sides to get b by itself
`b=6`.

Lastly, we have all our values and now just need the equation for the line which leaves us with
`y=3x+6`.

If you don't understand something or need more help, feel free to ask.