Find the equation of a line parallel to y = -4x + 2 passing through (2,3)

Analyze the question: We need a line parallel to y = -4x + 2 that passes through the point (2, 3).

Concept: Parallel lines have the same gradient (slope). The line y = -4x + 2 is in the form y = mx + c, so its gradient is m = -4. Our new line must also have m = -4.

Solution:

Use the point-slope form: y - y₁ = m(x - x₁)

y - 3 = -4(x - 2)

y - 3 = -4x + 8

y + 4x - 3 - 8 = 0

y + 4x - 11 = 0

Check: Substitute (2, 3): 3 + 4(2) - 11 = 3 + 8 - 11 = 0 ✓

Compare with the options:

• A: y + 4x + 11 = 0 → 3 + 8 + 11 = 22 ≠ 0 ✗
• B: gradient is +4, so not parallel ✗
• C: y + 4x - 11 = 0 → works ✓
• D: gradient is +4 ✗

Tip: For "parallel" questions, copy the gradient. For "perpendicular" questions, use the negative reciprocal. Then plug in the point to confirm. Checking the given point in each option is a fast way to eliminate wrong choices in the exam hall.