Problem Solving

Hi Everyone,

I ran across this problem. What is the fastest way to solve this problem, without mapping anything out...

IN a xy-coordinate plane, a line is defined by y=kx+1. If (4,b), (a,4) and (a,b+1) are three points on the line, where a and b are unknown, the k =
a. 1/2
b. 1
c. 1.5
d. 2
e. 2.5

Thanks!

b=4k+1
4=ak+1
b+1=ak+1
solving
k=1/2

xcusemeplz2009 wrote:b=4k+1
4=ak+1
b+1=ak+1
solving
k=1/2

dont get it! it seems too complicated!!

fruti_yum wrote:

xcusemeplz2009 wrote:b=4k+1
4=ak+1
b+1=ak+1
solving
k=1/2

dont get it! it seems too complicated!!

As per the question there are 3 points which are lying on the line,so they must satisfy the equation of the line. Putting the values we get
b=4k+1 --1
4=ak+1 ---2
b+1=ak+1 ----3

from 2 and 3, right hand side is same i.e ak+1
therefore b+1=4 ..> b=3
Substituting in equation 1, we get
3=4k+1
2=4k
1/2=k