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Solve Problems Using Ordered Pairs

Sep 26, 2022
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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 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.

What is an ordered pair?

Solve problems using ordered pairs

Example 1:

Identify ordered pair in the given grid.

example 1

Solution:

parallel

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.

step 3

So, ordered pair is (4, 2).

Example 2:

parallel

Graph data using below ordered pair on the grid.

x axis y axis

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 2

Step 3: Use a ruler to connect the points.

step 3

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.

example 3

Solution:

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

david stanley

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.

step 3

So, Stanley has 45 when David has 40.

Exercise

  1. Write ordered pairs from the graph.
Exercise 1

2. Write the ordered pairs from the graph.

Exercise 2

3. Identify the origin on the graph.

Exercise 3

4. Draw the graph using below table.

Exercise 4

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.

Exercise 6

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

Exercise 7

8. Draw the graph for the following order pairs.

Exercise 8

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.

Exercise 9

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

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.

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