What is the linear equation passing through the intersection and origin of two straight lines 3x + 2y-3 = 0 and 2x + y-6 = 0? How to determine the slope?

Find the intersection first
Two linear equations
(3-3x)/2=6-2x
3-3x=12-4x
x=9
y=-12
The intersection is (9, - 12)
Because the line goes through the origin
So the slope of the line = (- 12-0) / (9-0) = - 4 / 3
So the linear equation is y = - 4x / 3

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