Graphing linear equations on a coordinate plane can be really easy! Let’s go through it step by step.

Step 1: Understand the Equation

A linear equation usually looks like this: $y = mx + b$. Here’s what those letters mean:

• $m$ is the slope. This shows how steep the line is (we can think of it like "rise over run").
• $b$ is the y-intercept. This is where the line crosses the y-axis.

For example, in the equation $y = 2x + 3$, the slope is 2 and the y-intercept is 3.

Step 2: Plot the Y-Intercept

First, plot the y-intercept. Let’s use the equation $y = 2x + 3$:

1. Find the y-intercept point (0, 3) on the y-axis.
2. Mark a point there.

Step 3: Use the Slope

Next, use the slope to find more points. Since the slope is 2, you’ll move up 2 units and 1 unit to the right:

1. From (0, 3), go up 2 to (1, 5) and then to the right to (1, 5).
2. Plot this point on your graph.
3. You can also find points by going backward: from (0, 3), move down 2 to (–1, 1) and then left to (–1, 1).

Step 4: Draw the Line

Once you have a few points plotted, connect them with a straight line. Don’t forget to extend the line across the graph and add arrows at both ends. This shows the line keeps going forever!

Step 5: Check Your Work

To make sure you got it right, try picking some more values for $x$ and see what $y$ becomes. For example, if $x = 2$, then: $y = 2(2) + 3 = 7$. Plot the point (2, 7) to check that your line is correct!

With these steps, you'll be able to graph linear equations easily! Happy graphing!