Answer: 4x+y-6=0
Explanation:
To find the equation of the line that is parallel to 4x+y+1=0, we need to work in terms of slope-intercept form, which is y=mx+b.
4x+y+1=0 [subtract both sides by 4x]
y+1=-4x [subtract both sides by 1]
y=-4x-1
Our original equation is in terms of y=mx+b.
The properties of parallel lines is that they NEVER touch. Therefore the slope must be the same. The y-intercept can be different though.
y=-4x+b [plug in (1,2)]
2=-4(1)+b [multiply]
2=-4+b [add both sides by 4]
b=6
We can fill in our equation now.
y=-4x+6
We need to make our equation match the original, so let's manipulate it.
y=-4x+6 [add both sides by 4x]
4x+y=6 [subtract both sides by 6]
4x+y-6=0
Therefore 4x+y-6=0 is the answer.