If 2 lines cross at (a,b), why must linear combo pass thru

[dsuarez3]

if two lines in the plane intersect at (a,b), why is it that any linear combination of the two line formulas will be another line and why must it also pass through the point (a,B)? can you show me mathematical proof.

thank you for your help.

 

[stapel]

can you show me mathematical proof.

Legitimate tutors don't generally "do" students' work for them, but we're glad to help you find the answer! :wink:

if two lines in the plane intersect at (a,b), why is it that any linear combination of the two line formulas will be another line and why must it also pass through the point (a,B)?

Does the book really give the second point as having a different y-coordinate? Or is that second point actually the same as the first, so the "B" is actually a "b"? I will assume the latter. :!:

How does your book define a "linear combination" of two line equations? Please provide the word-for-word definition, along with all of your work and reasoning so far. Thank you!

Eliz.