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Mathematics

If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.

Straight Line Eq

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Answer

Given lines,

⇒ y = 3x + 7 and 2y + px = 3

⇒ y = 3x + 7 and 2y = -px + 3

⇒ y = 3x + 7 and y=−p2x+32y = -\dfrac{p}{2}x + \dfrac{3}{2}

Comparing above equations with y = mx + c we get,

Slope of 1st line = 3

Slope of 2nd line = −p2-\dfrac{p}{2}

Since,

Product of slopes of perpendicular lines = -1.

∴3×−p2=−1⇒−p=−1×23⇒−p=−23⇒p=23.\therefore 3 \times -\dfrac{p}{2} = -1 \\[1em] \Rightarrow -p = \dfrac{-1 \times 2}{3} \\[1em] \Rightarrow -p = -\dfrac{2}{3} \\[1em] \Rightarrow p = \dfrac{2}{3}.

Hence, p = 23\dfrac{2}{3}.

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