What value of \( m \) will make the lines \( 4x - 7y = 5 \) and \( 9x + my = 3 \) parallel?
Answer (2)
l : y = m 1 x + b 1 an d k : y = m 2 x + b 2 l ∣∣ k ⟺ m 1 = m 2 − − − − − − − − − − − − − − − − − − − − − − − − l : 4 x − 7 y = 5 → − 7 y = − 4 x + 5 → y = 7 4 x − 7 5 k : 9 x + m y = 3 → m y = − 9 x + 3 → y = − m 9 x + m 3 l ∣∣ k ⟺ − m 9 = 7 4 cross m u lt i pl y : 4 m = − 9 ⋅ 7 4 m = − 63 / : 4 m = − 15.75 ← an s w er
The value of m that makes the lines 4 x − 7 y = 5 and 9 x + m y = 3 parallel is − 15.75 . This is found by ensuring that the slopes of both lines are equal. We derived the slopes and set them equal to solve for m .
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