Finding and Graphing Points for Linear Relationships
Your students may have encountered ordered pairs last year, but it's a good idea to start by reviewing the basic skills of locating a point on a grid from an ordered pair. A day spent using grids to practice locating points that fall in a straight line will be a day well spent.
Materials: poster paper or a transparency and overhead projector for demonstration; straightedge
Preparation: Draw a large coordinate grid on the poster paper or transparency. Label the x- and y- axes from 0 through 10. Display the grid where students can see it.
Prerequisite Skills and Concepts: Students should know about ordered pairs and locating points on a grid.
- Write these ordered pairs on the board: (6,4); (7,5); (8,6); and (9,7). Point to the ordered pair (6,4).
- Ask: What rule describes the relationship between the numbers in this ordered pair?
Elicit from students this rule: the first number minus two equals the second number.
- Ask: Does the same rule apply to the other ordered pairs?
Students should realize that each ordered pair follows this rule. You can help them by using the rule to write each ordered pair as an equation on the board: 6 2 = 4, 7 2 = 5, 8 2 = 6, 9 2 = 7.
- Say: Let's locate these ordered pairs on a grid.
- Ask: How would you locate the point for (6,4) on the grid?
Students should say "to start at 0, move 6 units to the right, then 4 units up". Mark this point on the grid for the class to see.
- Have students verbalize how to locate the point for each of the other ordered pairs. Then mark each point on the grid. Emphasize the importance of moving right for the first number in the ordered pair and up for the second number.
- Ask: What figure do you think will be formed by connecting the points on the grid?
Students should see that a line will be formed. Use a straightedge to connect the points.
- Provide students with other examples of ordered pairs that follow a rule. Have students identify the rule and explain how to graph the points. Here is one example: rule: the first number plus three equals the second number; ordered pairs: (2,5); (3,6); (4,7); and (5,8)
Finding and Graphing Points
for Linear Relationships
Finding the Length of a Line