Question

are the lines in the figure parallel, perpendicular, or neither? choose 1 answer: a parallel b perpendicular c neither

Explanation:

Step1: Find slope of line a

Points on line a: (2, 0) and (6, 4). Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. So $m_a = \frac{4 - 0}{6 - 2} = \frac{4}{4} = 1$.

Step2: Find slope of line b

Points on line b: (-6, 9) and (0, 0). Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. So $m_b = \frac{0 - 9}{0 - (-6)} = \frac{-9}{6} = -1.5$? Wait, no, let's check again. Wait, the green dot on line b: let's take (0,0) and (-6, 9)? Wait, no, maybe better points. Wait, line b passes through (0,0) and let's see another point. Wait, the green dot on line b: x=-6, y=9? Wait, no, the grid: each square is 1 unit. Let's take (0,0) and (6, -9)? Wait, no, maybe I made a mistake. Wait, line a: (2,0) and (6,4): rise 4, run 4, slope 1. Line b: let's take (0,0) and (-6, 6)? Wait, no, the green dot on line b: x=-6, y=9? Wait, no, the y-axis: 8,6,4,2,0,-2,-4,-6,-8. So the green dot on line b: x=-6, y=9? No, 9 is above 8. Wait, maybe the green dot is at (-6, 9)? No, the grid lines: from y=8, then 6,4,2,0,-2,-4,-6,-8. So the green dot on line b: x=-6, y=9? That can't be. Wait, maybe the green dot is at (-6, 9) is wrong. Wait, let's look at line b: it goes from top left to bottom right, passing through (0,0). Let's take two points: (0,0) and (6, -6). Then slope is (-6 - 0)/(6 - 0) = -1. Wait, that's better. So (0,0) and (6, -6): slope -1. Then line a: (2,0) and (6,4): slope 1. Now, check if slopes are negative reciprocals: 1 and -1. The product of slopes: 1 * (-1) = -1. So lines are perpendicular.

Answer:

B. Perpendicular