Answer:
y = -5/3x or 5x +3y = 0
Explanation:
To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.
Slope
The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For the given points, the slope is ...
m = (5 -0)/(-6 -(-3)) = 5/(-3) = -5/3
Equation
The line trough the origin has a y-intercept of zero, so its equation will be ...
y = mx
For the slope we found, the desired equation is ...
y = -5/3x
Standard form
If we multiply by 3 and add 5x, we have ...
3y = -5x
5x +3y = 0 . . . . . . standard form equation of the line