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What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y + 1 = 0?

4 x + y + 6 = 0
4 x + y - 6 = 0
4 x - y - 6 = 0

User Nuri Akman
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1 Answer

4 votes

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.

User Tiago Fabre
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