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 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.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

step-by-step explanation: