Answer:
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