Question

Write the equation of a line that is BOTH PARALLEL and PERPENDICULAR

to
2x + 4y = 16 through ( 12,15)

Equation for the parallel line:
Equation for the perpendicular line:

Answer 1

Parallel line: y=-x+27

Perpendicular line: y=x+3

Explanation:

y=mx+b, where m is the slope and b is the y-intercept.

Rearrange '2x+4y=16' to fit this format:

2x + 4y = 16

x+y=8

y=-x+8

Parallel line

If two lines are parallel, they have the same slope. So our equation goes from y=mx+b to y=-x+b. We know the line goes through (12,15), so we sub this in to get b:

15=-12+b

b=27

So our equation is y=-x+27

Perpendicular line

If two lines are perpendicular, the slope of one line is the negative inverse of another: eg, if a line had slope=3, the line perpendicular to it would have slope=-1/3. The negative inverse of -1 is 1, so our equation goes from y=mx+b to y=x+b.We know the line goes through (12,15), so we sub this in to get b:

15=12+b

b=3

So our equation is y=x+3