How would you determine if lines intersected or not

if the lines were something like

y=-x-2

and

y=x^2+2-4

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- Jan 26th 2009, 12:29 PMwilliamintersection of lines
How would you determine if lines intersected or not

if the lines were something like

y=-x-2

and

y=x^2+2-4 - Jan 26th 2009, 02:02 PMShowcase_22
Well since you have two expressions involving x's and y's you can put them together.

$\displaystyle y=-x-2$ and $\displaystyle y=x^2+2x-4$ so $\displaystyle y=-x-2=x^2+2x-4$ by equating the y's.

So you need to solve $\displaystyle -x-2=x^2+2x-4$ to get the x co-ordinate. The y co-ordinate can then be found by substituting this x value into one of the two equations (they should give the same answer if you've done it right!). - Jan 26th 2009, 02:16 PMwilliam
- Jan 26th 2009, 11:22 PMShowcase_22
Exactly!

$\displaystyle

-x-2=x^2+2x-4

$

Here's the first step: $\displaystyle x^2+2x+x-4+2=0$. - Jan 27th 2009, 01:33 AMIsomorphism
- Jan 27th 2009, 04:24 AMwilliam
- Jan 27th 2009, 09:52 AMShowcase_22
Simultaneous equations are faster than just graphing them.

What if you have two lines that intersect at (100,1000000)? It would be very hard to draw a graph for that!