Answer:
lines are parallel
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines is - 1
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = 3, 1) and (x₂, y₂ ) = (8, 6)
m = [tex]\frac{6-1}{8-3}[/tex] = [tex]\frac{5}{5}[/tex] = 1 ← slope of line a
Repeat with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (2,9)
m = [tex]\frac{9-1}{2+6}[/tex] = [tex]\frac{8}{8}[/tex] = 1 ← slope of line b
Since both slopes are equal, line a and line b are parallel
