Determine whether the given lines are parallel, perpendicular, or neither.

Question

a) y + 5 = -12

x - y = 10

b) 3x - 5y = 10

10x + 6y = 36

c) y = 3

2y - 3 = 15

Please show your steps. If you want to answer one, tell me which one you answered.

Answer 1

For the lines to be parallel, they must have the same slope. For them to be perpendicular, they must have the negative reciprocal as a slope.

A)

y+5=-12

y=-7 (horizontal line)

x-y=10

y=x-10

Therefore the slope is neither the same nor negative reciprocal, so the answer is neither.

B)

3x-5y=10

5y=3x-10

y=(3/5)x -2

10x+6y=36

6y=-10x+36

y= (-5/3)x+6

In these case, the slopes are the inverse reciprocal of each other thus the lines are perpendicular.

C)

y=3 (horizontal line)

2y-3=15

2y=18

y=9 (horizontal line but 6 units higher)

In this case the slope is the same for both lines (0), so they are parallel.

Answer 2

a)

y = -17 vs y = x-10

the slope of the first line is zero..

the slope fo the second line is one..

Niether

b)

3x-10 = 5y

(3/5)x - 2 = y

6y = 36 - 10x

y = (-5/3)x + 6

the slope of the first line is 3/5

the slope of the second line is -5/3

they are perpendicular

(c)

the slope of both horizontal lines are

zero, so they are parallel