Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4

JAMB Mathematics 2023 51 views

Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0

  1. y = -⁵⁄₃ x – 2
  2. 3y = 2x + 5 ✓
  3. 3y = 5x – 2
  4. None of these

Explanation

Step 1: Find slope of given line
3x + 2y + 4 = 0
2y = -3x – 4
y = -3x/2 – 2
Slope m₁ = -3/2

Step 2: Find perpendicular slope
For perpendicular lines: m₁ × m₂ = -1
(-3/2) × m₂ = -1
m₂ = -1 ÷ (-3/2)
m₂ = 2/3

Step 3: Use point-slope form
Line passes through (2, 3) with slope 2/3
y – y₁ = m(x – x₁)
y – 3 = (2/3)(x – 2)

Step 4: Simplify
y – 3 = (2/3)x – 4/3
y = (2/3)x – 4/3 + 3
y = (2/3)x + 5/3

Step 5: Clear fractions
Multiply entire equation by 3:
3y = 2x + 5

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