Graphing the Ratio (Definition, Types and Examples) - BYJUS

# Graphing the Ratio

A coordinate plane is a two-dimensional plane formed by the intersection of the x-axis and the y-axis. We can use the coordinate plane to represent a comparison of quantities or ratios. Here we will learn the steps involved in the graphing of ratios of two quantities....Read MoreRead Less

## Ratio

A ratio is a pair of numbers that are compared. Part-to-part, part-to-whole, and whole-to-part comparisons are all examples of ratios. Units may or may not be included in the ratios.

## Coordinate Plane

A two-dimensional plane formed by the intersection of a vertical line which is called the y-axis and a horizontal line called the x-axis is known as a coordinate plane. These are a set of perpendicular lines that intersect at zero, which is known as the origin. The axes divide the coordinate plane into four sections, each of which is referred to as a quadrant.

## Graphing Ordered pair

Ordered pairs are used to graph and locate points on a coordinate plane. The ordered pairs are always in the (x, y) form where the first number is the x-coordinate and the second number is the y-coordinate. The first coordinate tells you how far to move along the x-axis, and the second coordinate tells you how far to move up or down the y-axis.

For example, to graph (4, 1), find 4 on the x-axis. Then move up 1 space. To graph (-3, 2), find -3 on the x-axis, then move up 2 spaces. To graph (3.5, -3), find 3.5 on the x-axis, then move down 3 spaces:

## How do we Graph a Ratio Relationship ?

Ordered pairs are used to graph and locate points on a coordinate plane. The ordered pairs are always in the (x, y) form where the first number is the x-coordinate and the second number is the y-coordinate. The first coordinate tells you how far to move along the x-axis, and the second coordinate tells you how far to move up or down the y-axis.

For example, to graph (4, 1), find 4 on the x-axis. Then move up 1 space. To graph (-3, 2), find -3 on the x-axis, then move up 2 spaces. To graph (3.5, -3), find 3.5 on the x-axis, then move down 3 spaces:

## Graphing the Ratio

All ratio tables follow a pattern. For a ratio of two quantities, equivalent ratios can be used to create ordered pairs of the form (first quantity, second quantity).

These ordered pairs can be plotted in a coordinate plane and a line drawn from point A to point B where A is the origin (0, 0).

Look for the x-coordinate on the x-axis as mentioned in the ordered pair. Then, if the y-coordinates are positive, move up the number of spaces equal to the y-coordinate (or move down if the y-coordinate is negative).

## Example

Example 1: Use the graph to represent the given relationship.

(a)

Table

2

4

6

Chair

3

6

9

(b)

Class

1

2

3

Students

10

20

30

Solution :

(a)

The ordered pairs (Tables, Chairs) are (2, 3), (4, 6), and (6, 9).

Make a graph of the ordered pairs. Draw a line through the points starting at (0, 0).

(b)

The ordered pairs (Class, Students) are (1, 10), (2, 20) and (3, 30).

Make a graph of the ordered pairs. Draw a line through the points starting at (0, 0).

Example 2: A man buys apples for $10 per pound. (a) Represent the statement in a ratio relationship using a graph. (b) How much will 3.5 pounds of apples cost? Solution: (a) Create a ratio table with apples (pound) and cost (dollar). Apple (Pound) 1 2 3 4 Cost (Dollar) 10 20 30 40 The ordered pairs (Apples, Cost) are (1, 10), (2, 20), (3, 30), and (4, 40). Make a graph of the ordered pairs. Draw a line through the points starting at (0, 0). (b) You can see from the graph that the price of 3.5 pounds is halfway between$30 and $40. Hence, 3.5 pounds of apples cost$35.

Alternative method:

We can find the cost of apples by using a double number line.

The first number line will represent the pounds, and the other will represent the cost per pound.

Example 3: Every two seconds, a man walks 4 meters. Every three seconds, a woman walks 5 meters. In the same coordinate plane, graph each ratio relationship. Who walks faster?

Solution:

Make a ratio table for the man and the woman. Then, using the graph, determine who walks faster by plotting the ordered pairs (Time, Distance) from the table.

Man

Time (Seconds)

Distance (Meters)

2

4

4

8

6

12

The ordered pairs for the man are (2, 4), (4, 8) and (6, 12)

women

Time

(seconds)

Distance

(meters)

3

5

6

10

9

15

The ordered pairs for the woman are (3, 5), (6, 10) and (9, 15).

Make a graph of the ordered pairs. Draw a line through the points starting at (0, 0) and label the points.

Both graphs start at the same point (0, 0). Since the man’s graph is steeper than the woman’s, the man walks faster.

Example 4: Every two seconds, a production machine produces 3 products. Every three seconds, the packaging machine packs 4 products. In the same coordinate plane, graph each ratio relationship. Which machine works faster?

Make a ratio for both the production and the packaging machine. Then, using a graph, determine which works faster by plotting the ordered pairs (time, distance) from the table.

Production Machinery

Time

(seconds)

Production

(per unit)

2

3

4

6

6

9

The ordered pairs for the production machinery  are (2, 3), (4, 6) and (6, 9)

Packaging Machinery

Time

(seconds)

Production

(per unit)

3

4

6

8

9

12

The ordered pairs for the packaging machinery are (3, 4), (6, 8) and (9, 12).

Make a graph of the ordered pairs. Draw a line through the points starting at (0, 0) and label the points.

Both graphs start at the same point (0, 0). Since the production graph is steeper than the packaging, the production machinery works faster.