SOLUTION: If the line represented by the equation 4x+ky-10=0 is perpendicular to the line with the equation 2x-10y+7=0, what is the value of k?

Algebra ->  Linear-equations -> SOLUTION: If the line represented by the equation 4x+ky-10=0 is perpendicular to the line with the equation 2x-10y+7=0, what is the value of k?      Log On


   

Question 1151417: If the line represented by the equation 4x+ky-10=0 is perpendicular to the line with the equation 2x-10y+7=0, what is the value of k?
Found 2 solutions by Edwin McCravy, MathLover1:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Put both equations in slope-intercept form
by solving for y

4x%2Bky-10=0
ky=-4x%2B10
Divide through by k
expr%28k%2Fk%29y+=+expr%28%28-4%29%2Fk%29x%2B10%2Fk
y+=+expr%28-4%2Fk%29x%2B10%2Fk
Comparing to 
y=mx%2Bb, 
the slope is
-4%2Fk

2x-10y%2B7=0
-10y=-2x-7
Divide through by -10
expr%28%28-10%29%2F%28-10%29%29y+=+expr%28%28-2%29%2F%28-10%29%29x-7%2F%28-10%29
y+=+expr%281%2F5%29x%2B7%2F10
Comparing to 
y=mx%2Bb, 
the slope is
1%2F5

To make them perpendicular,
1. Flip one of the slopes
2. Change its sign
3. Set it equal to the other slope.

I'll flip 
-4%2Fk,
change its sign, and get
k%2F4

Set it equal to 1%2F5

k%2F4=1%2F5

Cross-multiply:

5k=4

k=4%2F5

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the line represented by the equation
4x%2Bky-10=0+
ky=-4x%2B10+
y=-%284%2Fk%29x%2B10%2Fk+=>slope is m=-%284%2Fk%29
is perpendicular to the line with the equation
2x-10y%2B7=0
2x%2B7=10y
y=%281%2F5%29x%2B7%2F10=>slope is m%5B1%5D=1%2F5
perpendicular lines have slopes negative reciprocal to each other
m=-1%2Fm%5B1%5D
substitute both
-%284%2Fk%29=-1%2F%281%2F5%29.....solve for k
-%284%2Fk%29=-5.......both sides multiply by -1
4%2Fk=5
4=5k
k=4%2F5
so, the value of k is 4%2F5
y=-%284%2F%284%2F5%29%29x%2B10%2F%284%2F5%29+
y=-5x%2B25%2F2+ is perpendicular to y=%281%2F5%29x%2B7%2F10

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-5x%2B25%2F2%2C+%281%2F5%29x%2B7%2F10%29+