Answer:
m is parallel to n
Step-by-step explanation:
Calculate the slopes of m, n, p and q using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
• Parallel lines have equal slopes
• The product of the slopes of perpendicular lines = - 1
For line m
using (x₁, y₁ ) = (- 2, 7) and (x₂, y₂ ) = (3, 5) ← 2 points on the line
m = [tex]\frac{5-7}{3+2}[/tex] = - [tex]\frac{2}{5}[/tex]
For line n
using (x₁, x₂ ) = (- 5, 0) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line
m = [tex]\frac{-2-0}{0+5}[/tex] = - [tex]\frac{2}{5}[/tex]
For line p
using (x₁, y₁ ) = (6, 15) and (x₂, y₂ ) = (10, 5) ← 2 points on the line
m = [tex]\frac{5-15}{10-6}[/tex] = [tex]\frac{-10}{4}[/tex] = - [tex]\frac{5}{2}[/tex]
For line q
using (x₁, y₁ ) = (6, 15) and (x₂, y₂ ) = (0, 0) ← 2 points on the line
m = [tex]\frac{0-15}{0-6}[/tex] = [tex]\frac{-15}{-6}[/tex] = [tex]\frac{5}{3}[/tex]
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Checking the list
m ≠ parallel to q ( slopes are not equal )
q ≠ perpendicular to n ( product of slopes ≠ - 1 )
n ≠ parallel to q ( slopes are not equal )
p ≠ perpendicular to m ( product of slopes ≠ - 1 )
m is parallel to n ( slopes are equal )
p ≠ perpendicular to q ( product of slopes ≠ - 1 )
Thus m is parallel to n ← only one from list
