Strait line equation

Question

Find the value of k if the lines 3x-2y-1=0 and kx-6y+1=0 are perpendicular

Answer 1

Since the lines are to be perpendicular, their slopes must be opposite reciprocals of each other. So let's begin by rewriting each equation in slope-intercept form. So the first equation converts to y = 3/2 x - 1/2 and the second equation becomes y = k/6 x + 1/6.

Now we pull out the slopes and, since opposite reciprocals always multiply to give you a product of -1, we can multiply the two slopes and set the product equal to -1, so we have 3/2 • k/6 = -1. Multiplying the two fractions, we have 3k/12 = -1 which then gives us 3k = -12 and this gives us a k value of -4.