Question #4d894

2 Answers
Sep 22, 2017

#k = (-10)/3#

Explanation:

Rearranging #3x + 2y - 5 = 0# to fit the form #y = mx + c#:

#2y = -3x + 5#

#(2y)/2 = (-3x + 5)/2#

#y =(-3)/2x + 5/2#

So #m_1 = (-3)/2#

Rearranging #kx - 5y + 8 = 0# to fit the form #y = mx + c#:

#-5y = -kx - 8#

#5y = kx + 8#

#(5y)/5 = (kx + 8)/5#

#y = k/5x + 8/5#

So #m_2 = k/5#

If the lines are perpendicular then we know that the gradients must be opposites of each other (#m_2= -1/(m_1)#)

So:

#k/5= -1/((-3)/2)#
#k/5= (-2)/3#
#k = (-10)/3#

Sep 22, 2017

The slope of the straight line
#3x + 2y - 5= 0 or y = -3/2x+5/2=0# is #m_1=-3/2#.

Again the slope of the straight line
#kx -5y +8= 0 or y = k/5x+8/5=0# is #m_2=k/5#.

As the straight lines are perpendicular to each other then

#m_1xxm_2=-1#

#=>-3/2xxk/5=-1#

#=>k=10/3#