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

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Solution

y = 3x + 7

Slope of this line = 3

2y + px = 3

2y = -px + 3

y = $fraction numerator negative p over denominator 2 end fraction x plus 3 over 2$

Slope of this line = $fraction numerator negative p over denominator 2 end fraction$

Since the lines are perpendicular to each other, the product of their slopes is -1.

$3 open parentheses fraction numerator negative p over denominator 2 end fraction close parentheses equals negative 1 fraction numerator 3 p over denominator 2 end fraction equals 1 p equals 2 over 3$

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