Question

Determine whether the graphs of these equations are parallel, perpendicular, or neither; with explanation please.

1. y = 4x + 5
-4x + y = -13

2. y = 7/8
x = -4

3. 3x + 6y = 12
y-4=-1/2(x+2)

Answer 1

Parallel lines have the same coefficients for x's and y's, they differ on constant terms such that...
line 1: \(A_1x+B_1y=C_1\)
line 2: \(A_2x+B_2y=C_2\)
and \(A_1=A_2\) as well as \(B_1=B_2\), but \(C_1\ne C_2\)...also the slopes \(m_1=m_2\).

Answer 2

Perpendicular lines have an interchanged coefficients for x's and y's such that...
line 1: \(Ax+By=C_1\)
line 2: \(Bx+Ay=C_2\)
... also their slopes are negative reciprocal of one another such as \[m_1=-\frac{1}{m_2}\] Another case is the vertical line \((x=A)\) and a horizontal line \((y=B)\), obviously they are perpendicular to each other.

Answer 3

If neither the case of parallel lines nor perpendicular lines are met, then it's neither parallel nor perpendicular....
Hope this will help you answer your problems from 1 to 3. \(\ddot\smile\)