Answer:
The answer to your question is below
Step-by-step explanation:
Data
Two lines are parallel if their slopes are the same.
Two lines are perpendicular if their slopes are reciprocal.
If there is no relation between the slopes of two lines they are neither parallel nor perpendicular.
Process
1.- Find the slope of the line given
-3x + 5y = -15
5y = 3x - 15
y = [tex]\frac{3}{5}[/tex] x - 3
Slope = [tex]\frac{3}{5}[/tex]
2.- Find the slopes of the other lines
a) 5x + 3y = 15
3y = -5x + 15
y = -[tex]\frac{5}{3}[/tex] + 5
slope = -[tex]\frac{5}{3}[/tex] This line is perpendicular to the line given
because the slopes are reciprocal.
b) 3x + 5y = 15
5y = -3x + 15
y = - [tex]\frac{3}{5}[/tex] x + 15 This line is neither parallel nor
slope = -[tex]\frac{3}{5}[/tex] perpendicular
c) -3x + 5y = 15
5y = 3x + 15
y = [tex]\frac{3}{5}[/tex]x + 15
slope = [tex]\frac{3}{5}[/tex] This line is parallel to the line given
d) 3x + 5y = 15
5y = -3x + 15
y = [tex]\frac{-3}{5}[/tex] + 3
slope = [tex]\frac{-3}{5}[/tex] This line is neither parallel nor perpendicular to the line given
