The slope of parallel lines is the same.
The line given 2y - 4x + 4= 0
=> 2y = 4x - 4
=> y = 2x - 2
The slope is 2
The equation of the line passing through the origin and parallel to the line is y/x = 2
=> y - 2x = 0
The equation of the required line is y - 2x = 0
First we will write the equation into the slope for,.
==> y-y1 = m(x-x1) such that (x1,y1) is any point passes through the line and m is the slope.
==> Given that the line passes through the origin, then the line passes through the point (0,0)
==> y- 0 = m(x-0)
==> y= mx..........(1)
now let us determine the slope.
We know that the line 2y-4x + 4 = 0 is parallel to our line.
Let us rewrite into the slops form.
==> 2y= 4x-4
==> y= 2x-2
Then the slope m = 2.
==> Then the equation of the line is written y= 2x OR it is written y-2x = 0