Question

For what value of k are the graphs of `12y= -3x+ 8` and `6y= kr- 5` parallel? For what value of k are they perpendicular?

Answer 1

Parallel at `" "color(blue)"k = -3/2"`
Perpendicular at `" "color(blue)"k=24"`

Explanation:

the given equations are `12y=-3x+8` and `6y=kx-5`

Writing them first in Slope-Intercept forms

`y= -3/12 x+8/12" "`and `y=k/6 x-5/6`

If they are parallel then slopes are equal,...therefore

`-3/12=k/6`

and `color(red)"k=-3/2"`

If they are perpendicular then the product of the slope `=-1`

`-3/12*k/6=-1`

and `color(red)"k = 24"`

God bless....I hope the explanation is useful.