Question

Does anyone know how to solve and find out the answer? Thank you so much if you help!

Answer 1

The lines are perpendicular.

Explanation:

`3x -2y=4`

Step 1: Add -3x to both sides.

`3x-2y+-3x=4+-3x`

`-2y=-3x+4`

Step 2: Divide both sides by -2.

`(-2y)/(-2) =(-3x+4)/(-2)`

`y=(3)/(2) x-2`

Finally...

`y=(3)/(2) x-2\\eq y=-(2)/(3) x+5` so the lines are not parallel.

However,
`(3)/(2)` is the opposite reciprocal of
`-(2)/(3)`, so, the lines are perpendicular.

(You can also try drawing the lines.)

Answer 2

perpendicular

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = -
`(2)/(3)` x + 5 ← is in slope- intercept form

with slope m = -
`(2)/(3)`

3x - 2y = 4 ( subtract 3x from both sides )

- 2y = - 3x + 4 ( divide through by - 2 )

y =
`(3)/(2)` x - 2 ← in slope- intercept form

with slope m =
`(3)/(2)`

• Parallel lines have equal slopes.

clearly the slopes are not equal, so not parallel.

• the product of the slopes of perpendicular lines = - 1

-
`(2)/(3)` ×
`(3)/(2)` = - 1

then the lines are perpendicular to each other.