Question

Find the equation of the line perpendicular to y= 3x - 6 that runs through the point (-1, -3).

Answer 1

Answer:

The equation of the line is;

$y=-\frac{1}{3}x-\frac{10}{3}$

Explanation:

Given that the line is perpendicular to the equation;

$y=3x-6$

So, the slope of the line will be the negative inverse of the slope of the equation above;

$m=-\frac{1}{3}$

Also, the line passes through the point;

$(-1,-3)$

Applying the point-slope form of linear equation;

$y-y_1=m(x-x_1)$

Substituting the values of the slope and coordinates;

$\begin{gathered} y-(-3)=-\frac{1}{3}(x-(-1)) \\ y+3=-\frac{1}{3}(x+1) \\ y+3=-\frac{1}{3}x-\frac{1}{3} \\ y=-\frac{1}{3}x-\frac{1}{3}-3 \\ y=-\frac{1}{3}x-3\frac{1}{3} \\ y=-\frac{1}{3}x-\frac{10}{3} \end{gathered}$

Therefore, the equation of the line is;

$y=-\frac{1}{3}x-\frac{10}{3}$