Which of the following planes is parallel to ABCD

P

1

:4x−2y+6z=3

P

2

=4x−2y−2z=6

P

3

=−6x+3y−9z=5

P

4

=2x−y−z=3

Step-by-step explanation:

The coefficients of each x,y,z give the direction vector of the normal vector of the plane.

Parallel but not identical condition will be that:

x

2

x

1

=

y

2

y

1

=

z

2

z

1



=

c

2

c

1

where each term is the coefficent of x,y,z respectively.

By observation we see P

2

and P

3

are parallel but not identical.

correct answers below:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)