The equation of the line that passes through the points (-6,-3) and (0,0) is y= -x/2
<u>Step-by-step explanation:</u>
It is given that,
The line passes through the point (-6, -3).
This point is represented as (x1,y1) which is equal to (-6,3).
The equation of the line can be given in the form y-y1 = m(x-x1).
where,
- x1 = -6 and y1 = 3
- m is the slope of the line.
<u>The slope of the line is given by the formula :</u>
Slope = (y2-y1) / (x2-x1)
Here, there is no other point given in the question.
So, let us assume that the line passes through the origin (0,0) = (x2,y2)
Slope = (0-3) / (0+6) = -3/6
Slope = -1/2
Therefore, m= -1/2
Now, substitute m= -1/2 and x1= -6 and y1 = 3 in the equation of line,
⇒ y-3 = (-1/2) (x+6)
cross multiplying 2 to the left side of equation,
⇒ 2y-6 = -x-6
⇒ 2y = -x-6+6
⇒ y = -x/2
The equation of the line is y= -x/2
