Mathematics Equation of Line

Let the slope of the required equation be m and the y-intercept be p
So, the x-intecept is 2p.

Using the fact that the line passes through (6,2), then the equation of the line:
y-2=m(x-6)
y=mx+(2-6m)...(*)

Since the x-intercept and y-intercept are 2p and p respectively, sub (2p,0) and (0,p):
0=m(2p)+(2-6m) => (6-2p)m=2 => m=1/(3-p)...(**)
p=2-6m...(***)

Sub (***) into (**):
m=1/(3-(2-6m))
m=1/(1+6m)
6m^2+m-1=0
m=1/3 or m=-1/2

Hence, the required equations are y=(1/3)x or y=(-1/2)x+5.


2010-09-10 21:12:47 補充：
Alternative method:
From (*), the x-intercept=(6m-2)/m and y-intercept=2-6m
Since the x-intercept is twice of the y-intercept, then:
(6m-2)/m=2(2-6m)
6m-2=4m-12m^2
12m^2+2m-2=0
m=1/3 or m=-1/2, which is same as the result of above solution.