Consider the lines

y = 3x + 5

2y = 4x + 5

3y = x - 2

2y = 3x - 2

4y = x - 5

Let's say that a pair of lines is good if the two lines are either parallel or perpendicular to each other. Among all the pairs of lines shown, how many pairs are good?

Guest Feb 6, 2022

#1**+2 **

How many pairs are good?

**Hello Guest!**

a y = 3x + 5 m = 3

b 2y = 4x + 5 m = 2

c 3y = x - 2 m = 1/3

d 2y = 3x - 2 m = 3/2

e 4y = x - 5 m = 1/4

No pairs are good.

!

asinus Feb 6, 2022

#2

#3**+2 **

**Hello Guest #2!**

I have isolated y in all lines: I divide the line by the y-coefficient.

The x-coefficient is the slope of the line.

If two lines have the same slopes,

they are a good pair. Parallel course.

If two lines have the same, slope and negative reciprocal of the slope,

then they are a good pair. Perpendicular course

!

asinus
Feb 6, 2022