Question

choose 1 answer:
a parallel
b perpendicular
c neither

Explanation:

Step1: Calculate slope of line a

Let two points on line a be $(0, - 2)$ and $(4,3)$. Using slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_a=\frac{3-( - 2)}{4 - 0}=\frac{5}{4}$.

Step2: Calculate slope of line b

Let two points on line b be $(-6,7)$ and $(0,-5)$. Using slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_b=\frac{-5 - 7}{0-( - 6)}=\frac{-12}{6}=-2$.

Step3: Check parallel - perpendicular condition

Parallel lines have equal slopes, $m_a
eq m_b$. Product of slopes of perpendicular lines is - 1, $m_a\times m_b=\frac{5}{4}\times(-2)=-\frac{5}{2}
eq - 1$.

Answer:

C. Neither