WAEC 2023 Mathematics · Question 22
A line L passing through the point (6, -13) is parallel to the line which passes through (7, 4) and (-3, 9). Find the equation of the line L.
Options
- A.y =
- B.y =
- C.y =
- D.y =
Answer: C. y =
Explanation written with AI and checked against the answer key
Analyze the question: Line L passes through (6, -13) and is parallel to the line through (7, 4) and (-3, 9). Parallel lines have equal gradients, so we find the gradient of the given line first. Concept: Gradient m = (y₂ − y₁)/(x₂ − x₁), and the equation of a line through (x₁, y₁) is y − y₁ = m(x − x₁). Step 1: Gradient of the given line m = (9 − 4)/(−3 − 7) = 5/(−10) = −1/2 Step 2: Gradient of L Since L is parallel to this line, its gradient is also m = −1/2. Step 3: Equation of L through (6, −13) y − (−13) = −1/2 (x − 6) y + 13 = −1/2 x + 3 y = −1/2 x + 3 − 13 y = −1/2 x − 10 Check: When x = 6, y = −3 − 10 = −13 ✓ Tip: For parallel lines, copy the gradient. For perpendicular lines, the product of gradients is −1. Always substitute the given point back into your final equation to check quickly. Options A and D have the wrong gradient sign, and B has the wrong intercept, so a quick check of the gradient and one point eliminates them.AI can make mistakes. Report anything that looks wrong.
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