What is the equation of a line that passes through the origin and is perpendicular to the line 2y=4x-6y+4?

y = - 2 x

Step-by-step explanation:

The catch to this one (and there is a catch) is that the y intercept is at 0,0.

All you need is the slope and that means you have to solve the equation for y

2y = 4x - 6y + 4 Add 6y to both sides

2y + 6y = 4x + 4 Combine terms on the left

8y = 4x + 4 Divide by 8

y = 4x/8 + 4/8 Reduce 4/8 to 1/2

y = 4x/8 + 1/2

y = 1/2 x + 1/2

Nowyou are all set to answer the question.

m1 * m2 = - 1

m1 = 1/2 because the coefficient in front of the x is the slope (5/8 in this case). m1 and m2 are both slopes.

1 / 2 * m2 = - 1 multiply both sides by 2

(1/2) * (2) * m2 = - 1 * (2)

m2 = - 2

The slope of the equation you want is - 2

y = - 2 x is the answer

The graph below shows the two equations.