Line equation .What is the equation of the line perpendicular to y=2x-3 and that passes through (0;0) ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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