# intersection of lines

• Jan 26th 2009, 12:29 PM
william
intersection 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 PM
Showcase_22
Well since you have two expressions involving x's and y's you can put them together.

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

So you need to solve $-x-2=x^2+2x-4$ 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 PM
william
Quote:

Originally Posted by Showcase_22
Well since you have two expressions involving x's and y's you can put them together.

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

So you need to solve $-x-2=x^2+2x-4$ 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!).

would i just collect like terms and factor or how would i solve that?
• Jan 26th 2009, 11:22 PM
Showcase_22
Exactly!

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

Here's the first step: $x^2+2x+x-4+2=0$.
• Jan 27th 2009, 01:33 AM
Isomorphism
Quote:

Originally Posted by william
How would you determine if lines intersected or not

if the lines were something like

y=-x-2

and

y=x^2+2-4

As far as I know y = x^2 + 2x - 4 is not a line... Its a parabola :D
• Jan 27th 2009, 04:24 AM
william
Quote:

Originally Posted by Isomorphism
As far as I know y = x^2 + 2x - 4 is not a line... Its a parabola :D

AH YES! thank you i could simply graph both and see where they intersect,if anywhere
• Jan 27th 2009, 09:52 AM
Showcase_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!