Thread: Straight line equation

What is the equation of the line that intersects line y = mx + b
at point (1, m+b)?

"The" line?

Originally Posted by Wilmer

What is the equation of the line that intersects line y = mx + b
at point (1, m+b)?

This question makes no sense: at any point in the (real euclidean) plane there infinite lines that contain that point.

Tonio

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.

Originally Posted by Wilmer

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.

Well, perhaps: what's the line that passes through (1,m+b) and has a slope equal to m?

Tonio

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

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 !!