Question

The lines represented by the equations y + 3/2x = -6 and 3y – 2x = -24 are

parallel
neither parallel nor perpendicular
perpendicular
the same line

Answer 1

The lines represented by the equations
`y + 3/2x = -6` and
`3y - 2x = -24` are neither parallel nor perpendicular.

To determine the relationship between the lines represented by the equations
`y + 3/2x = -6` and
`3y - 2x = -24,`

The slope-intercept form
`(y = mx + b),` where m is the slope and b is the y-intercept.

For
`y + 3/2x = -6:`

`y = -(3)/(2)x -6`

The slope (m) is -3/2.

For
`3y - 2x = -24:`

`3y = 2x - 24`

`y = 2/3x - 8`

The slope (m) is 2/3.

Since the slopes are different (-3/2 and 2/3), the lines are not parallel.

To determine if they are perpendicular, we can check if the product of their slopes is -1.

However, in this case, the product is not -1 (-3/2 * 2/3 = -1).

Therefore, the lines are neither parallel nor perpendicular.

Answer 2

Neither Parallel nor Perpendicular

Explanation:

Convert 3y - 2x = -24 to slope - intercept form

3y - 2x = -24

3y = -24 + 2x

3y = 2x - 24

y = 2/3x - 8

They are neither parallel or perpendicular

Parallel lines have the same slope, but these are different

Perpendicular lines have the opposite inverse (negative reciprocal) slope, but these are just reciprocals

-Chetan K