## Lesson: Graphing Integers Introducing the Concept

Students learned about linear equations earlier. Now they will review how to solve those equations and learn how to graph linear equations in x and y.

Materials: overhead transparency or poster paper

Preparation: Draw a coordinate grid on a transparency or poster paper, or use Learning Tool 20 in the Learning Tools Folder.

Prerequisite Skills and Concepts: Students should know how to graph ordered pairs. They should also be able to solve simple addition, subtraction, multiplication, and division linear equations.

Write the equation x − 3 = y on the board.

• Ask: Who could tell me what this equation means in words?
Students should say, “One number minus 3 is equal to another number,” or something equivalent.
• Say: Earlier in the year we worked with similar equations, but those equations had only one unknown, an x or a y. This equation has two unknowns, x and y. If I were to let x = 2 in this equation, what would the value of y be?
Students will calculate that y = -1. Draw a table with four columns. Label the first column x, the second column x − 3 = y, the third column y, and the fourth column (x, y). See the table below.
 x x − 3 = y y (x, y)

Put 2, 2 − 3 = -1, -1, and (2, -1) in the appropriate columns of the first row, as in the table shown.

 x x − 3 = y y (x, y) 2 2 − 3 = -1 -1 (2, - 1)
• Say: Since y = -1 when x = 2, I put 2 in the x-column, 2 − 3 = -1 in the x − 3 = y column, -1 in the y-column, and the ordered pair (2, -1) in the (x, y) column.
Solicit four or five other values for x and find their corresponding values for y. List them in the table accordingly.
• Say: We now have two ways to represent the relationship between the numbers x and y. The equation describes a general relationship between the numbers; in words, the equation states that one number minus 3 is equal to another number. The table now gives us some specific values that satisfy the relationship. If you look at the table, you will see that every y-value is 3 less than its corresponding x-value.
• Say: Now we are going to look at a third way to represent the equation x − 3 = y. This way is a visual representation, using a graph. We are going to use the values from our table and graph the ordered pairs on the graph.
• Ask: Using this graph (the overhead or large poster graph), who can show us where the point (2, -1) is located?
Have a student graph the point on the grid. Do the same for the other points in the table.