Question

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.

3x=4y-5 and 2/3 y=x/2+8

Answer 1

The lines are parallel

The graph in the attached figure

Explanation:

we have

`3x=4y-5` ---> equation A

`(2)/(3)y=(x)/(2)+8` -----> equation B

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Find the slope of the line A

`3x=4y-5`

Isolate the variable y

Adds 5 both sides

`4y=3x+5`

Divide by 4 both sides

`y=(3)/(4)x+(5)/(4)`

The slope is

`m_A=(3)/(4)`

step 2

Find the slope of line B

`(2)/(3)y=(x)/(2)+8`

Multiply by 6 both sides to remove the fractions

`4y=3x+48`

Divide by 4 both sides

`y=(3)/(4)x+(48)/(4)`

Simplify

`y=(3)/(4)x+12`

The slope is

`m_B=(3)/(4)`

step 3

Compare the slopes

we have

`m_A=(3)/(4)`

`m_B=(3)/(4)`

so

`m_A=m_B`

therefore

The lines are parallel

see the attached figure to better understand the problem