Question

How can i know if two lines/equations intersect on a graph, algebraically? For example, I have two equations:

1. -x^2 + 3x + 4, and
2. x - 4

Ty in advan.

Answer 1

Equations need an "equal" sign and usually consist of both x and y terms.
Did you mean y = -x^2 + 3x + 4 and y = x-4 ?

Make a table of values for each one.
The first one is a downwards opening parabola, get about 4 or 5 points and you should see the general shape of it.
The second is a straight line, so you need only 2 points.
You should see that they intersect at two points

For an algebraic solution, set the y's equal to each other.
x-4 = -x^2 + 3x + 4
x^2 - 2x - 8 = 0
solve this quadratic, (hint: it factors nicely)

compare your algebraic answer to your graphic answer, they of course must be the same.