Question

1. use the slopes of lines a and b to show that they are perpendicular to each other. see example 2

Explanation:

Step1: Find slope of line A

Pick two points on line A, say (0, - 1) and (2, 3). Using slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_A=\frac{3-( - 1)}{2 - 0}=\frac{4}{2}=2$.

Step2: Find slope of line B

Pick two points on line B, say (0, 5) and (5, 0). Using slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_B=\frac{0 - 5}{5 - 0}=\frac{-5}{5}=-1$.

Step3: Check perpendicular - condition

Two lines are perpendicular if the product of their slopes is - 1. Calculate $m_A\times m_B=2\times(-1)=-1$.

Answer:

Since the product of the slopes of line A and line B is - 1, the two lines are perpendicular.