Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −2x+3y=12? drag each choice into the boxes to correctly complete the table. parallel perpendicular neither -2x+y=12 3x+2y=-2 y=2/3x-1 -2x+3y=11

We are given first equation: −2x+3y=12.

Converting it in slope-intercept form

3y=2x + 12

y= 2/3 x + 12/3

y= 2/3 x + 4.

Slope of the given equation is 2/3.

Note: When slopes are same, lines would be parallel.

When slope are negative reciprocals, lines would be perpendicular.

When neither same nor negative reciprocal, the lines neither parallel nor perpendicular.

1) First option : -2x+y=12.

In slope-intercept form y = 2x +12.

Slope is 2 there.

2) 3x+2y=-2

In slope-intercept form y = -3/2 x - 1.

Slope = -3/2.

Slope are negative reciprocal to slope of −2x+3y=12 equation.

3) y=2/3x-1

Slope = 2/3.

4) -2x+3y=11

y = 2/3 x + 11/3.

10000

step-by-step explanation: divide by 2,