Determine if graph of a pair of lines are parallel

Question

x+10=4

y-x=-6

Answer 1

x + 10 = 4
y - x = -6

 

We isolate our values:

x = -6

y = x - 6

 

No, they are not parallel. The first line is just straight across. No matter what we put in for y, x will always equal -6

The second equation has a slope value of 1, so it will be continuously rising at that rate (1 rise to 1 run).

Answer 2

x+10=4 will be a vertical line where x is -6: Subtract 10 from each side and get x=-6

 

while y-x=-6 will be a line slanted at 45 degrees (a slope of 1): Subtract x from both sides to get y=x-6

 

The two lines will intersect at (-6,-12), meaning that they are not parallel.