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?

1 Answer

Answer:

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.