The Coordinate Plane: Lesson 2 - Graphing Equations

Graphing Equations is the second of four self-paced lessons in the “The Coordinate Plane” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson focuses on representing linear equations as a graphed line.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, students need to answer questions that require them to understand that equations can be represented as graphs of linear equations.

They need to understand that solutions to equations with two variables can be written as ordered pairs in the form (x, y) and represented in a table.

They will also need to know that the ordered pairs in a table can be plotted as points and connected with a line on a graph.

This lesson focuses on representing linear equations as a graphed line. Students will need to have a basic understanding of equations and substituting for x and y values.

On the GED Mathematics Test, students may need to recognize either a line based on an equation, or they may need to select an equation that matches a graphed line.

2Creating a Table from an Equation

Watch the video for an explanation of how to use formulas to solve for X and Y.

Solving for X and Y

Video: 1m 34s

An equation can have more than one variable. Consider the equation y = x + 3. There is a relationship between the variables y and x. The value of y depends on the value of x.

By substituting different values for x, you can find possible values for y. Possible solutions for an equation, for example y = x + 3 shown below, are expressed as ordered pairs (two coordinates) in a table.

Question What x and y coordinates complete the table at left to show ordered pair solutions for the equation y = 2x + 5?

Step 1 Fill in the missing y-coordinate in the second row. Substitute 1 for x, then solve for y.

y = 2x + 5

y = 2(1) + 5 ← substitute 1 for x

y = 2 + 5

y = 7 ← ordered pair is (1, 7)

Step 2 Fill in the missing x-coordinate in the third row. Substitute 5 for y, then solve for x.

y = 2x + 5

5 = 2x + 5 ← substitute 5 for y

5 – 5 = 2x + 5 – 5 ← subtract 5 from both sides to isolate 2x

0 = 2x

0 ÷ 2 = 2x÷ 2 ← divide both sides by 2 to solve for x

0 = x ← ordered pair is (0, 5)

Answer Row 2 y = 7 Row 3 x = 0

3Graphing the Equation

Solutions to an equation with two variables can be shown in a table or as a list of ordered pairs. Then the values can be shown as plotted points. Here are some values for y = x + 3.

The line through the points is the graph of the equation. If the graph is a straight line, the equation is a linear equation.

Question Find another ordered pair on the graph above. Show that it is a solution of the equation y = x + 3.

Step 1 Look for places where the graph meets grid intersections.

The graph meets grid intersections at (–3, 0) and at (–4, –1)

Step 2 Write the first coordinate. You moved 3 units to the right on the x-axis. You moved in the positive direction.

For (–3, 0):

y = x + 3

0 = –3 + 3 ← substitute 0 for y and –3 for x

0 = 0 ← the pair (–3, 0) makes the equation true

For (–4, –1):

y = x + 3

–1 = –4 + 3 ← substitute –1 for y and –4 for x

–1 = –1 ← the pair (–4, –1) makes the equation true

Answer Both ordered pairs (–3, 0) and (–4, –1) are solutions of the equation y = x + 3.

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, consider how you would work through them with your students.

How could you help students determine if a point is a solution to the equation in Graph B?

The Coordinate Plane: Graphing Equations Skill Review

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Printable Resource

In this lesson you have learned about graphing equations. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.