I chose to do this because it’s new and will probably be important for later.

To do a quick review of inequalities, they are expressions that compare 2 values. It’s like an equation, but the equal sign is replaced with different symbols.

Solving inequalities is like solving equations, but graphing is a bit different.

Specifically, we are going to be looking at the inequalities with 2 variables, giving us a x and y axis.

To make our initial line, it’s pretty simple. Start as you do usually, I like setting x to 0 to find the y intercept and start graphing from there.

From here, we can do the classic rise over run. Since x has a coefficient of 5 (5/1), we go up 5, and right 1.

The graph will look like this.

Obviously, so far we just graphed an equation. There’s no inequality.

To be able to graph inequalities we need to understand a few things.

1. The type of line. if the sign is a regular greater than/less than sign, the line will be dotted. If the sign is a greater than or equal to/ less than or equal to sign, the line will be filled. This is to show whether or not the line itself is considered a solution.
2. Filling the right side of the graph. We need to distinct the solutions from the non-solutions. We do this by coloring/filling the area that has solutions. We can do a test on the inequality. Choose a point, like (0,0) to put into the inequality. If the inequality stays true after having input the point, then the side of the line with that point will have the solutions.

As we can see, this inequality is not true, so the solutions will be on the other side of the line.

To sum it up, the graph will have a dotted line, and the shaded area will be on the other side of the line relative to (0,0).