Determine whether the graphs of each pair of equations are p

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.

y = -3, y = -7

2y = 8, 3(2 + x) = 3(y +2)

Please solve and show your work and explain whether the problem is parallel, perpendicular or neither. Thank you!

1) Solution: The equations of straight lines are

3x+6y=1 ------------(1)

y=(1/2)x ------------(2)

We know that , the equation of line slope-intercept form is

y=mx+b where \'m\' is the slope and b= y- intercept

Now equation (1) becomes ----> y= - (1/2)x +(1/6)

Therefore

slope of (1) is m1= -(1/2)

Slope of (2) is m2= 1/2

The slopes of equations (1) & (2) are neither equal nor their product is equal to -1 . i.e m1.m2=(-1/2)(1/2)=-1/4-1

Therefore

The equations (1) & (2) are neither parallel nor perpendicular.

2) Solution:

The equations of straight lines are

y= -3 -------------(1)

y= - 7 ------------(2)

Both lines are horizontal

Therefore, they are parallel to each other.

3)Solution:

The equations of straight lines are

2y=8 --------> y=4 --------(1)

3(2 + x) = 3(y +2) --------> y=x --------(2)

Now equation (1) is horizontal and equation (2) neither horizontal nor vertical.

The equations (1) & (2) are neither parallel nor perpendicular.