## 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

- 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.

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