How can you determine if two lines are perpendicular? How can you tell if two lines are parallel? State whether the following sets of lines are parallel, perpendicular or intersecting. Then explain why.

Question

1) y = x + 4
y = x - 3
2) y = 3x - 7
y = -1/3 x + 10
3) y = 3x -7
y = -3x + 10

Answer 1

Two lines are parallel if they have the same slope
Two lines are perpendicular if their slopes are the opposite reciprocals of each other.

since all your equations are in the form
y = mx + b, and m is the slope,

you can find your result by just looking at them.

Answer 2

Reiny, you stated, i can find my result by just looking at them, but I'm not exaclty sure about that.
1) y = x + 4
y = x - 3
2) y = 3x - 7
y = -1/3 x + 10
3) y = 3x -7
y = -3x + 10
I've gotten different answers on whether the sets of lines are
parallel, perpendicular or intersecting. My first answer is that all the sets are parallel, but then I second guessed myself and said all the 1st line of each set is parallel and the 2nd lines are perpendicular. Can you confirm if my 1st answer is correct, if not, why?

Answer 3

Remember that:
"y = mx + b, and m is the slope, "

For the first one:
1) y = x + 4
y = x - 3
"Two lines are parallel if they have the same slope "
Knowing that "x" is a short form for "1x" where slope=m=1, can you deduce whether they have the same slope?

You can take it from here for the rest.