▶️ Answer/Explanation
Answers:
(a) \( y = -2x – 7 \)
(b) \( y = \frac{1}{2}x \)
(a) \( y = -2x – 7 \)
(b) \( y = \frac{1}{2}x \)
Explanation:
(a) Equation of line AB:
1. Find slope (m): \( m = \frac{y_2 – y_1}{x_2 – x_1} = \frac{-3 – 5}{-2 – (-6)} = \frac{-8}{4} = -2 \).
2. Find y-intercept (c): Using point A (-6, 5), substitute into \( y = mx + c \):
\( 5 = -2(-6) + c \) → \( c = -7 \).
3. Final equation: \( y = -2x – 7 \).
(b) Perpendicular line through origin:
1. Slope of perpendicular line: Negative reciprocal of -2 → \( \frac{1}{2} \).
2. Since it passes through (0,0): \( y = \frac{1}{2}x \) (no y-intercept term needed).