Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines = - 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
All the equations given are in slope- intercept form
y = 2x + 1 → with m = 2
y = [tex]\frac{1}{2}[/tex] x - 4 → with m = [tex]\frac{1}{2}[/tex]
y = x + 1 → with m = 1
y = - [tex]\frac{1}{x}[/tex] x - 3 → with m = - [tex]\frac{1}{2}[/tex]
y = 10 + x → y = x + 10 → with m = 1
Thus
y = x + 1 and y = 10 + x are Parallel since both have m = 1
y = 2x + 1 and y = - [tex]\frac{1}{2}[/tex] x - 3 are Perpendicular since 2 × - [tex]\frac{1}{2}[/tex] = - 1
