Lesson: Finding and Graphing Points for Linear Relationships
Developing the Concept
At this level, students will begin to see the relationship between equations and straight-line graphs on a coordinate grid.
At this level, students will begin to see the relationship between equations and straight-line graphs on a coordinate grid.
Materials: poster paper or a transparency and overhead projector for demonstration; straightedge; Coordinate Grid Worksheet (PDF file), a straightedge, and lined paper for each student
Preparation: Draw a coordinate grid on poster paper or a transparency. Label the x- and y-axes from 0 through 10. Make copies of the Coordinate Grid Worksheet (PDF file) for students, or use Learning Tool 51 in the Learning Tools Folder.
Prerequisite Skills and Concepts: Students should know about ordered pairs and locating points on a grid. They should also be able to recognize and interpret an equation.
- Write the equation x + 5 = y on the board.
- Ask: How could you say this equation in words?
Students should say that the equation means “a number plus five equals another number,” or some comparable statement. - Draw a table with four columns and five rows on the board. Have students draw their own table. Label the first column x, the second column x + 5, and the third column y. Leave the fourth column blank for now. Write 1 in the first column below x.
x x ÷ 5 y Ordered Pair 1 - Ask: What happens to the equation if we replace x with 1? Elicit from students the equation 1 + 5 = 6. Write 1 + 5 in the second column below x + 5. Then write 6 in the third column below y.
x x ÷ 5 y Ordered Pair 1 1 ÷ 5 6 - Continue to replace x with 2, 3, then 4. Have students complete the first three columns of their tables on their own. Ask for a volunteer to complete the table on the board.
- Say: Let's write ordered pairs using the values of x and y. Label the fourth column of your table Ordered Pair. Remind students that when they locate points on a grid, they first move right on the x-axis, and then up on the y-axis. Therefore, the first number in an ordered pair is a value for x, and the second number is a value for y. These numbers are called the x- and y-coordinates.
- Ask: What is the first number we used for x? (1) What is the first number we calculated for y? (6) So, what is the first ordered pair? (1, 6)
Have students complete their tables. When they are finished, record the ordered pairs in the table on the board.
x x ÷ 5 y Ordered Pair 1 1 ÷ 5 6 (1, 6) 2 2 ÷ 5 7 (2, 7) 3 3 ÷ 5 8 (3, 8) 4 4 ÷ 5 9 (4, 9) 5 5 ÷ 5 10 (5, 10) - Say: Now we're going to graph the equation x + 5 = y on a grid. (Point to the grid you made.) This grid is called a coordinate grid. Let's take a closer look at the different parts of the grid.
- Point to the horizontal line on the grid.
- Say: This line is called the x-axis.
- Point to the vertical line on the grid.
- Ask: What do you think this line is called?
Students should make the connection to the y-axis. - Say: Now, let's locate the ordered pairs on the grid. Who can find (1, 6)?
Have a volunteer describe the location of the ordered pair. Mark the location on the coordinate grid at the front of the class. Then have students locate the rest of the ordered pairs on their own grids.
- Say: Let's connect all of the points. What figure did we make?
Have students use a straightedge to connect the points. Show students how extending both ends of the line slightly, and drawing arrows, shows that the line goes on in both directions. Students should identify the figure as a straight line. - Have students repeat this activity with the equation x − 2 = y. Use the numbers 5, 6, 7, 8, and 9 for x.
Wrap-Up and Assessment Hints
These skills will need lots of practice. Reinforce the need for students to work carefully so their graph is accurate. When you assess students' progress, keep the number of exercises small enough that they have time to complete each step without rushing.