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Question

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


Solution

Given line equations,
$$y = 3x + 7$$
Slope of this line $$= 3$$

And,
$$2y + px = 3$$
$$2y = -px + 3$$
$$y = (-p/2) + 3$$
So, the slope of this line $$= -p/2$$

For these two lines to be perpendicular to each other, the product of their slopes must be $$-1.$$
$$(3) \times (-p/2) = -1$$
$$3p/2 = 1$$
$$p = 2/3$$

Maths

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