Yes, as mentioned, when you graph an inequality (involves shading), a broken line is when you don't have "or equal to."
When you graph an equation, any point on that line is a solution. When you graph a system of equations, any point along each line is a solution for that equation, but where they cross is the solution for BOTH, thus the solution for the system of equations.
If you graph an inequality like y > 5, the entire line has a y-value of 5, so nowhere on the line is a solution. Any point in the shaded region is a solution.
If, however, you had y ≥ 5, anywhere along the line is a solution, along with anywhere in the shaded region.
That's a way to check your work, also, to make sure you've shaded the right area. Let's say you had x + y > 5.
y > -x + 5
You know how to graph that, and one of the points on our line is (0,5), the y-intercept.
5 > -0 + 5
5 > 5
0 > 0
Well, that's certainly not true! That's why we need the dotted line.
Let's pick (0,6), though, above our dotted line.
6 > -0 + 5
6 > 5
1 > 0
Hey that's true, so we know the shaded area is above our dotted line.
