# Write the equation of the line that passes through the origin and parallel to 2y-4x+4 = 0

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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