A line $y = m x + 1$ is parallel to a line $3 x + y + 1 = 0$ when $m = a$ and perpendicular to the same line when $m = b$ . Find the product of $a$ and $b$ .
-1

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Solution

The correct option is A -1
Two lines are parallel when their slopes are equal.

The slope of a line $y = m x + c$ is 'm'.

$3 x + y + 1 = 0 \to y = - 3 x - 1$

If $y = m x + c$ is parallel to $y = - 3 x - 1$ ,
m = slope of $y = - 3 x - 1$ = -3
So, a = -3

Two lines are perpendicular when the product of their slopes is -1.

So. $b \times - 3 = - 1 \to b = \frac{1}{3}$

$a \times b = - 3 \times \frac{1}{3} = - 1$

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