SOLUTION: Find the value of k so that the line containing the points (-4,k) and (8,-4) is perpendicular to the line y=2/5x+4. If you could explain how I should start this problem. I thought

Algebra ->  Linear-equations -> SOLUTION: Find the value of k so that the line containing the points (-4,k) and (8,-4) is perpendicular to the line y=2/5x+4. If you could explain how I should start this problem. I thought       Log On


   

Question 654493: Find the value of k so that the line containing the points (-4,k) and (8,-4) is perpendicular to the line y=2/5x+4. If you could explain how I should start this problem. I thought if it is perpendicular I would use the opposite reciprocol, but considering I have an unknown variable(k) not quite sure what to do with it. Thanks for your time!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of k so that the line containing the points (-4,k) and (8,-4)
is perpendicular to the line y=2/5x+4.
:
The slope of the given equation: m1 = 2%2F5
Find the slope (m2) of the given coordinates
The slope formula m = %28y2-y1%29%2F%28x2-x1%29
Assign the values as follows
x1=-4, y1=k
x2=8, y2=-4
m2 = %28-4-k%29%2F%288-%28-4%29%29 = %28%28-4-k%29%29%2F12
:
We know the slope relationship between perpendicular lines is m1*m2 = -1
2%2F5*%28%28-4-k%29%29%2F12 = -1
cancel 2 into 12
1%2F5*%28%28-4-k%29%29%2F6 = -1
%28%28-4-k%29%29%2F30 = -1
multiply both sides by -30, also gets rid of all those negatives
4 + k = 30
k = 30 - 4
k = 26
:
Use this value for y1, find the slope (m2) of the new equation,
Find the equation using the point/slope formula, y-y1 = m(x-x1)
See that it is perpendicular to y = 2%2F5x + 4