Solve Problems Using Ordered Pairs

Key Concepts

• Solve Problems Using Ordered Pairs

Introduction

What is an origin?

The point at which the x-axis and the y-axis intersect is called the origin.

What is an ordered pair?

Ordered pairs are made up of two numbers. The first number is the X-coordinate and the second number is the Y-coordinate.

Solve problems using ordered pairs

Example 1:

Identify ordered pair in the given grid.

Solution:

Step1: Mark a point on the grid.

Step2:  The first number be the X-coordinate along with the distance from the origin, i.e., 4.

Step3: The second number be the Y-coordinate, along with the distance from the origin, i.e., 2.

So, ordered pair is (4, 2).

Example 2:

Graph data using below ordered pair on the grid.

Solution:

From the given table, the ordered pairs are:

(0, 0) (1, 2) (3, 6) (4, 8).

Step 1: Graph the first point (0, 0)

Graph the second point (1, 2)

Start at (0, 0) move 1 unit to the right along the x-axis. Then move 2 units up.

Step 2: Plot the rest of the order pairs from the table.

Step 3: Use a ruler to connect the points.

Example 3:

David and Stanley’s earnings are shown week wise in the table. David starts with no money, but Stanley starts with $5. How much will Stanley have when David has $40? Graph the data on the grid.

Solution:

Make a table showing how much money David and Stanley have after each week.

Let us consider,

David earnings = X-axis

Stanley earnings = Y-axis

Step 1: Plot the ordered pairs from the table.

 (0, 5) (5, 10) (10, 15) (15, 20) (20, 25) (25, 30)

Step 2: Draw a line to show the pattern.

Step 3: Extend the line to the point where X-coordinate is 40. The corresponding Y-coordinate is 45.

So, Stanley has 45 when David has 40.

Exercise

1. Write ordered pairs from the graph.

2. Write the ordered pairs from the graph.

3. Identify the origin on the graph.

4. Draw the graph using below table.

5. Draw a graph to the given order pairs. 

       (0, 0) (1, 2) (3, 6) (4, 8) (5, 10) (6, 12)

6. Join the dots using a ruler.

7. Identify the order pairs from the graph and join the dots using a ruler.

8. Draw the graph for the following order pairs.

9. Thomas has a summer job mowing lawns. He is paid $5 per hour. The amount he can earn in 4 hours is shown in the function table. Show the hours worked on the x-axis, and the dollars earned on the y-axis. Graph the data.

10. Bayan feeds her puppy, Buster, 2 cups of food each day. Bayan made this table to show how much food Buster eats for 1, 2, 3, and 4 days. Graph the ordered pairs (days, food). Describe the Bayan graph.

Concept Map

What have we learned

• Understand the coordinate system and origin.
• Identify the order pairs from the graph.
• Draw the graph using data and plot the ordered pairs.
• Solve the problem using ordered pairs.