Question

Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −2x+3y=6 ? Drag and drop each choice into the boxes to correctly complete the table.
Parallel Perpendicular Neither

options:
-3x - 2y = 4
-2x + 3y = -6
2x + 3y = 6
-2x + 3y = 0

Answer 1

Answer:

2x+3y=6

Is parallel to the given line

...........................

Answer 2

Answer:

Parallel:

-2x + 3y = -6

-2x + 3y = 0

Perpendicular:

-3x - 2y = 4

Neither:

-2x + 3y = -6

Step-by-step explanation:

1. First, rearrange the first equation so it is in slope-intercept form.

Top equation: y=2/3x+2

In this case, the slope is 2/3. If an equation is parallel, the slope is the same. If it is perpendicular, it should be the opposite reciprocal. And if it's neither, it doesn't match any of those.

2. Now rearrange the rest of the equations.

a. y= -3/2x-2

b. y=2/3x-2

c. y= -2/3x+2

d. y= 2/3x

3. Now determine the slopes for each equation

a. m= -3/2

b. m=2/3

c. m= -2/3

d. m= 2/3

4. Now compare the slopes of these equations to the slope of the first equation, which is m=2/3

a. it's not parallel (-3/2≠2/3), it's perpendicular because -3/2 is the opposite reciprocal of 2/3

b. it's parallel because 2/3=2/3

c. it's not parallel (-2/3≠2/3), it's not perpendicular (3/2≠2/3), so it's neither

d. it's parallel because 2/3=2/3