Question

Find the equation of the line through the origin with slope -6 Answer: 6x+y=0

Answer 1

The equation of the line with the slope has the form

$y=kx+b$

According to the problem, $k=\tan\alpha=-6,$

then $y=-6x+b$ .

The line goes through the origin  $O(0,0)$ , hence

substitute coordinates of the origin into the equation of the line:

$0=-6\cdot0+b,\\ b=0.$

The equation of the line is

$y=-6x,\\ 6x+y=0.$