How do you turn these into a parallel and perpendicular equation?

Question

1.y=4x+2

2.y=2/7x+1

3.y=-1/2x+1

4.y=-9x-13

Answer 1

Adding on to Arturo, an example would be:

 

y = 4x + 2

 

A parallel line will have the same slope and a different y-intercept, so one possible answer is y = 4x + 4

 

A perpendicular line will have a slope that is the negative inverse of the given slope and the same or a different y-intercept, so one possible answer is y = -¼ x + 4

Answer 2

Look at the slope m of each line.  A parallel line will have the same slope m, but can have a different y-intercept b.  A perpendicular line has a slope m' = -1/m, and can have a different y-intercept b.  The choice of y-intercept b is arbitrary, unless your are given a point (x₁,y₁) that the line goes through.  In that case, once you have the correct slope m, get the y-intercept from

 

y₁ = mx₁ + b' ⇒ b'= y₁ - mx₁ 

 

Then you will have a final equation for the line:

 

y = mx + b' (parallel)

 

or

 

y = (-1/m)x + b' (perpendicular)