graphing equations?!?!?!?

Question

how do I find out if a graphing equation has no solution,one solution or infinatley many solutions

equation example:y= -x
y=2x

Answer 1

First you arrage the formula so it looks like y= #x + # or y= #x - #. (You're allowed to have a fraction) It's supposed to look like the slope formula (y=mx+b).
m is the slope, b is the y intercept, so the number before x is going to be the slope. The number on it's own is the y-intercept. These are the numbers you focus on.

If the slopes are the same, but the y-intercepts are different, the lines are parallel and thus have no solution.

If the slopes are the same and they have the SAME y-intercept, there are infinite solutions becuase it's one line ontop of another.

If both are different, then there is one solution.

So for y=2x, it would be y=2x+0. So your slope is 2, y-intercept is 0.
y= -x is y=-x+0. slope is -1, y-intercept is 0.
There should be one solution.

Answer 2

well the ones that u put are linear which means all solutions. if u see one that's like x(x+3)=0, then the answers are 0 and -3 (u take the opposite of w/e is in the parenthesis to make it equal 0 for one solution, and 0 for one if it's a variable outside parentheses)

another kind is like 3/x-7, in which case the answer would be all real #s excluding 7, cuz the denominator can never equal zero (it would be undefined). there's also: (the square root of) x+5, the answer would be all real #s excluding those less than 5, cuz u cant take a square root of a # less than 0 (undefined).

hope this helps!