What is Standard Form? Ax + By = C Where A, B, and C are real ...

There <strong>is</strong> several ways to graph linear equations in two variables. For now we will focus on using<br />

the x <strong>and</strong> y intercepts to graph the lines which <strong>are</strong> in st<strong>and</strong>ard form.<br />

Before we begin, let's quickly review what st<strong>and</strong>ard form looks like!<br />

<strong>What</strong> <strong>is</strong> <strong>St<strong>and</strong>ard</strong> <strong>Form</strong>?<br />

<strong>Ax</strong> + <strong>By</strong> = C<br />

<strong>Where</strong> A, B, <strong>and</strong> C <strong>are</strong> <strong>real</strong> numbers, A & B both not 0.<br />

Examples: 2x + 4y = 8<br />

5x – 10y = -20<br />

Now let's review what the term intercepts means! An intercept <strong>is</strong> where your line crosses an<br />

ax<strong>is</strong>. We have an x intercept <strong>and</strong> a y intercept.<br />

The point where the line touches the x ax<strong>is</strong> <strong>is</strong> called the x intercept.<br />

The point where the line touches the y ax<strong>is</strong> <strong>is</strong> called the y intercept.<br />

Take a look at the graph below.<br />

If we can find the points where the line crosses the x <strong>and</strong> y ax<strong>is</strong>, then we would have two points<br />

<strong>and</strong> we'd be able to draw a line. How many points determine a line? ________________<br />

When equations <strong>are</strong> written in st<strong>and</strong>ard form, it <strong>is</strong> preferred to find the intercepts. Take a look at<br />

th<strong>is</strong> diagram, as it will help you to underst<strong>and</strong> the process.

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Now, let's apply th<strong>is</strong>. Just remember:<br />

To find the X Intercept: Let y = 0<br />

To find the Y Intercept: Let x = 0<br />

Key: We organize our x <strong>and</strong> y intercepts in a table called a “T-Bar table” cons<strong>is</strong>tent with the<br />

above. We always begin with the following T-Bar <strong>and</strong> then we fill in the m<strong>is</strong>sing coordinates.<br />

Let's look at an example 1.<br />

Graph 2x + 4y = 8 by first finding the x <strong>and</strong> y intercepts.<br />

Let’s complete the T-Bar table. (See page below for steps.)

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Example 1. Graph 2x + 4y = 8 by first finding the x <strong>and</strong> y intercepts.<br />

The completed T-Bar <strong>is</strong><br />

Key: The x <strong>and</strong> y intercepts <strong>are</strong> the two points which determine the line!