1. ## showing

Show that the intersection point of $\displaystyle y=-x+1$ and $\displaystyle x=2b$ lies on the line $\displaystyle y=m(x-2b)+(1-2b)$

2. ## Re: showing

what is your progress so far?

3. ## Re: showing

What, exactly, is the intersection point of y= -x+ 1 and x= 2b? Does it satisfy the equation y= m(x- 2b)+ (1- 2b)? And is that "for some m" or "for all m"?

4. ## Re: showing

Originally Posted by HallsofIvy
What, exactly, is the intersection point of y= -x+ 1 and x= 2b? Does it satisfy the equation y= m(x- 2b)+ (1- 2b)? And is that "for some m" or "for all m"?
the exact intersection point is when y=1-2b

when y=1-2b, for y= m(x- 2b)+ (1- 2b),

1-2b=m(x- 2b)+ (1- 2b)
m(x-2b)=0

5. ## Re: showing

Originally Posted by Punch
the exact intersection point is when y=1-2b

when y=1-2b, for y= m(x- 2b)+ (1- 2b),

1-2b=m(x- 2b)+ (1- 2b)
m(x-2b)=0
To put it more simply,
the point of intersection of the lines

y=1-x and x=2b is $\displaystyle (2b,\;1-2b)$

Now to show that this point lies on the other,
simply insert the co-ordinates to see that equality is maintained.