4x+6=y-2x y=-1/6x+22?

Question

State whether each pair of lines is parallel, perpendicular, or neither. Explain why.

Answer 1

4x+6=y-2x y=-1/6x+22
+2x +2x
y=6x=6

These lines are perpendicular because the slope are recipricals of each other and they are opposite in that one is positive and one is negative.

Answer 2

Write them in form y = mx + b:

4x + 6 = y - 2x => y = 6x + 6

y = -1/6 x + 22 is already in standard form.

Gradients are therefore 6 and -1/6. Parallel lines have the same gradient, perpendicular lines have gradients multiplying to -1. So in this case the lines are clearly perpendicular.

Answer 3

You should be able to answer this by solving both equations for y. One is already solved for y, so that makes it so much easier.

Then ask yourself, how do I know if lines are parallel. Then see if that situation exists. If not, ask yourself, how do I know if lines are perpendicular? Then see if that situation exists. If neither exists, then the answer is neither.

Now, hopefully no one just answers this for you. Go to your book or notes and look up how to determine if lines are parallel or perpendicular. I'm serious! The book tells you how to determine if the lines are parallel or perpendicular.

Hint: It involves the slopes.

Update:
AGH! People gave the answer while I was writing this up.

Answer 4

y=mx+b where m is the slope.

so, 4x+6=y-2x is y=6x+6 with a slope of 6.

and, y=-1/6x+22 has a slope of -1/6.

so, they are perpendicular

Answer 5

4x+6= -1/6x+22
4x+1/6x= 22-6
24x/6+x/6= 24

25 x=24X6
25x=144
x=144/25
4x+6=y-2xy
4 X 144/25= y-2 X 144/25 X y
4 X 144/25= y ( 1-144/25)
y= [ 4 X 144/25]/ (1-144/25)
this is the easy way!!!!!
good luck calculating!