The product of the slope of two perpendicular lines is -1.
For the line y = 2x - 3, the slope is 2, the slope of the line perpendicular to this is -1/2
As the perpendicular pass through (0,0)
(y - 0) / (x - 0) = -1/2
=> 2y = -x
=> x + 2y = 0
The required equation of the line is x + 2y = 0
Two lines are perpendicular when the product of their slopes is -1. Comparing the given equation to the point slope form of an equation of a line, we'll get the slope m1 = 2.
y = mx + n
y = 2x - 3
We also know that:
m1*m2 = -1, where m2 is the slope of the perpendicular line.
m2 = -1/m1
m2 = -1/2
The equation of the perpendicular line, that passes through the origin and has the slope m2 is:
y - 0 = m2(x - 0)
y = -x/2
y = -0.5x