What is the equation of the line that intersects line y = mx + b

at point (1, m+b)?

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- June 8th 2011, 06:15 PMWilmerStraight line equation
What is the equation of the line that intersects line y = mx + b

at point (1, m+b)? - June 8th 2011, 07:30 PMTKHunny
"The" line?

- June 8th 2011, 07:31 PMtonio
- June 8th 2011, 08:24 PMWilmer
Ok (quite simple); was looking for y = bx + m as the unique answer:

lines y = mx + b and y = bx + m intersect at (1, m+b);

how should I word the question ? Thanks. - June 9th 2011, 03:05 AMtonio
- June 9th 2011, 07:23 AMWilmer
Thanks you guys who answered; this I guess requires a li'l more explaining.

To start, I would have rather posted this in "puzzle" section, but was told

to post it here by a moderator; again, probably because I wasn't clear!

During the hockey game Monday night when Boston demolished Vancouver 8=1,

I was (during commercials...) playing around with graph paper : straight lines.

I graphed line y = 5x + 3 (m=5, b=3) ; some points on it: (0,3), *(1,8), (2,13) ....

Bored, I decided to see what happens if I switch m and b, thus y = bx + m,

so y = 3x + 5 (m=3, b=5); some points on it: (0,5), *(1,8), (2,11) ....

Now I noticed that the 2 lines intersect at point *(1,8) : or at (1, b+m).

I graphed a few other cases: intersection always (1, b+m).

Of course, from the 2 equations we have equality mx + b = bx + m,

which leads to x = 1 ; then to y = m + b.

So, without further ado, I put up my question...

SORRY for not being clearer (Crying)

Btw, any suggestions as to how to "word" this differently will be appreciated.

Like:

Line#1 (y = mx + b) and Line#2 intersect at point (1, b+m).

Using same variables (x,y,m,b), what is Line#2's equation?

Looks like I need to get a life !!