Answer:
line L is not parallel to AB
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3y = 4 - 2x ( divide terms by 3 )
y = [tex]\frac{4}{3}[/tex] - [tex]\frac{2}{3}[/tex] x ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
Calculate slope of AB using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(1, 3) and (x₂, y₂ ) = B(- 2, - 1)
[tex]m_{AB}[/tex] = [tex]\frac{-1-3}{-2-1}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
Parallel lines have equal slopes
Since the slopes are not equal then the lines are not parallel
