Question

Write an equation for a line that is perpendicular to the line 8x-4y=12 and passes throught the origin

Answer 1

y= -
`(1)/(2)`x

Explanation:

First, let's put the line in y=mx+b form

8x-4y=12

Subtract 8x over

-4y= -8x+12

Then divide everything by -4

y=2x-3

To find the perpendicular slope, negate the slope and flip the numerator and the denominator

Original Slope: 2/1

Flip: 1/2

Negate: -1/2

Then, use the point slop formula to find the equation of the line.

(y-
`y_(1\\)`)=m(x-
`x_(1)`)

Insert (0,0) in for
`x_(1) y_(1)` and -1/2 in for m

y-0= -1/2(x-0)

Distribute the -1/2

y-0= -1/2x+0

Add the 0 over

y= -1/2x