To graph linear equations in standard form, which looks like (Ax + By = C), it's important to know what each part means. Here, (A), (B), and (C) are numbers, while (x) and (y) are the variables we will work with.

Step 1: Change to Intercept Form

A good way to graph the equation is to change it to slope-intercept form, which is (y = mx + b). In this form, (m) is the slope (how steep the line is) and (b) is the y-intercept (where the line crosses the y-axis).

For example, let’s take the equation (2x + 3y = 6). We can rearrange it to find the slope-intercept form:

• Start by moving (2x) to the other side: (3y = -2x + 6).
• Now, divide by 3: (y = -\frac{2}{3}x + 2).

Step 2: Find Key Points

Now we’ll find some important points to help us graph.

First, find the y-intercept. This is where the line crosses the y-axis, and you can find it by setting (x = 0):

• In our example, when (x = 0), (y = 2). So, we have the point ((0, 2)).

Next, let’s find another point by setting (y = 0):

• For the equation (2x + 3(0) = 6), we simplify to get (2x = 6), which gives us (x = 3). So, our second point is ((3, 0)).

Step 3: Plot Points and Draw the Line

Now, we can plot the points ((0, 2)) and ((3, 0)) on the graph.

Grab a ruler and draw a straight line through these points. Extend the line across the grid.

And just like that, you’ve successfully graphed a linear equation in standard form!