Question

The equation of the line perpendicular to $y=3x+5$, passing through the point (-1,-2) is .

• A. x+3y+7=0
• B. y=3x+1
• C. 2x+3y+8=0

Answer 1

The correct option is A x+3y+7=0

Given line is $y=3x+5$

Slope of the line = 3.

Let the equation of the required line be $y=mx+c$, where m is the slope and c is the y-intercept.

Since the required line is perpendicular to the given line,
$m\times 3=-1$
$\Rightarrow m=-\frac{1}{3}$

The equation of the required line is $y=-\frac{1}{3}x+c$.

The line passes through (-1,-2)

Thus, $-2=-\frac{1}{3}\times (-1)+c$
$\Rightarrow c=-\frac{7}{3}$

Hence, the equation of the required line is
$y=-\frac{1}{3}x--\frac{7}{3}x$
$-3y=x+7$
$x+3y+7=0$