Graphing is a great way to see solutions for linear inequalities. When we create a graph of an inequality, it helps us find all the possible values that meet the requirement.

What Are Linear Inequalities?

Let’s look at this linear inequality:
$y < 2x + 3.$
To graph it, we first draw the line for the equation $y = 2x + 3$. We use a dashed line because the inequality is strict, meaning the points on the line don’t count.

Shading the Right Area

Now, we need to decide where to shade. Since we have $y < 2x + 3$, we will shade below the line. The shaded area shows all the possible pairs of $(x, y)$ that satisfy the inequality.

An Example

For example, let’s take $y \leq -x + 4$. Here, we graph the line $y = -x + 4$ using a solid line, because this inequality includes points on the line. Then, we shade below this solid line.

Final Thoughts

By graphing these inequalities, we can see not just one solution, but many solutions. This makes it easier to understand how the variables relate to each other. This method is also helpful in solving real-life problems where we need to keep track of limits or boundaries.