Answer:
[tex]y=3x+6[/tex]
Step-by-step 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 [tex]-y=-3x+6[/tex]. We then want to isolate y by dividing by -1 on each side to get the new equation [tex]y=3x-6[/tex]. 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 [tex]y=3x+b[/tex]. Our line goes through a certain point therefore our x and y values are given so that our equation looks like [tex]-6=3(-4)+b[/tex]. We now simplify to get [tex]-6=-12+b[/tex] and add 12 on both sides to get b by itself [tex]b=6[/tex].
Lastly, we have all our values and now just need the equation for the line which leaves us with [tex]y=3x+6[/tex].
If you don't understand something or need more help, feel free to ask.
