Graphing linear inequalities might seem hard at first, but it's really easy once you follow a few simple steps. Let’s go through it together.

Step 1: Know the Inequality Symbols

First, let's look at the different inequality symbols. Here’s what they mean:

• $>$ means "greater than"
• $<$ means "less than"
• $\geq$ means "greater than or equal to"
• $\leq$ means "less than or equal to"

Step 2: Change to Slope-Intercept Form

Next, we change the linear inequality to slope-intercept form. This means writing it like $y = mx + b$. In this formula, $m$ is the slope, and $b$ is where the line crosses the y-axis.

For example, take the inequality $2x + 3y < 6$. We need to solve for $y$. Here’s how you do it:

$$3y < -2x + 6$$

Then divide everything by 3:

$$y < -\frac{2}{3}x + 2$$

Step 3: Draw the Boundary Line

Now, it’s time to draw the boundary line. For the equation $y = -\frac{2}{3}x + 2$, first plot the y-intercept at the point $(0, 2)$. Then, use the slope to find another point. From $(0, 2)$, go down 2 and to the right 3.

Since our inequality is "less than," we draw a dashed line. This dashed line shows that we do not include the points on the line itself.

Step 4: Shade the Correct Area

Finally, we need to shade the right side of the line. Choose a point that is not on the line. A good choice is usually $(0, 0)$.

Now, plug this point into the original inequality. If the point satisfies the inequality, shade the side that includes $(0, 0)”. If not, shade the other side.

And that’s it! With these steps, you’ve learned how to graph linear inequalities!