SOLUTION: If the points (4,2) and (-1,k) are on a line that is perpendicular to the line y=2x+1, what is the value of k? * Please write in clear Algebric form so I can apply the same met

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If the points (4,2) and (-1,k) are on a line that is perpendicular to the line y=2x+1, what is the value of k? * Please write in clear Algebric form so I can apply the same met      Log On


   

Question 1006535: If the points (4,2) and (-1,k) are on a line that is perpendicular to the line y=2x+1, what is the value of k?
* Please write in clear Algebric form so I can apply the same method to other problems similar to this one. I really appreciate your help. Thanks!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If the points (4,2) and (-1,k) are on a line that is perpendicular to the line y=2x%2B1, what is the value of k?
the line y=2x%2B1 has a slope 2
a line that is perpendicular to the line y=2x%2B1 will have a slope -1%2F2 (negative reciprocal)
so, its equation, so far, is y=-%281%2F2%29x%2Bb
since it passes through the points (4,2) , we will use it to find b
y=-%281%2F2%29x%2Bb
2=-%281%2F2%294%2Bb
2=-2%2Bb
b=4
so, equation is:
y=-%281%2F2%29x%2B4

now use (-1,k) to find k which represents y coordinate

k=-%281%2F2%29%28-1%29%2B4
k=1%2F2%2B4
k=1%2F2%2B8%2F2
k=9%2F2
so, the point is (-1,k) =(-1,9%2F2)