Graphs

Types of Graphs, Plotting, Interpreting, and Real-World Contexts

CAPS Grade 10 Mathematical Literacy

This document serves as a comprehensive guide to the Graphs subtopic in the Grade 10 Mathematical Literacy CAPS curriculum. It outlines the types of graphs you need to know, the process of plotting and drawing them, how to interpret the stories they tell, and common contexts in South Africa where these graphs are applicable.

1. Types of Graphs You Must Know

Linear (Straight Line) Graphs

Linear graphs depict direct proportional relationships where there is a constant difference.

Example: If you earn a constant hourly rate, your total earnings can be represented as a straight line graph.

Horizontal Lines

Horizontal lines indicate a fixed cost or a value that remains unchanged over time.

Example: A flat monthly subscription fee, where the cost does not vary regardless of usage.

Inverse Proportion Curves

These curves illustrate a relationship where one variable increases while the other decreases.

Example: When a prize is shared among more people; the more individuals involved, the less money each person receives.

Discrete vs. Continuous Graphs

Discrete Graphs (Dotted)

Used for variables that cannot be divided into fractions, such as counting people or cars.

Continuous Graphs (Solid Line)

Represent variables that can be measured in decimals, such as time, distance, or litres.

Test Yourself: Types of Graphs

4 Questions

1 A graph showing a fixed monthly cell phone contract fee of R100 is a:

Linear graph

Horizontal line

Inverse curve

Discrete graph

2 A graph showing the number of people (cannot have half a person) should be:

Continuous (solid line)

Discrete (dotted/points)

Linear

Horizontal

3 As the number of workers increases, the time to complete a job decreases. This is a(n):

Linear graph

Horizontal line

Inverse curve

Discrete graph

4 Earning R50 per hour is shown as a:

Linear graph (straight line)

Horizontal line

Inverse curve

Discrete graph

0/4

2. Plotting and Drawing

Labeling Axes

Independent Variable on x-axis, Dependent Variable on y-axis.

Choosing a Scale

Select consistent scale that fits the grid.

Title

Every graph should have a clear descriptive title.

Example Graph Setup

Title: Distance Traveled Over Time

x-axis: Time (hours)

y-axis: Distance (km)

Scale: x-axis: 1 cm = 1 hour, y-axis: 1 cm = 10 km

Graph Reading Challenge

Find values from the graph description.

A linear graph shows cost (y) vs litres (x). The rule is: Cost = R15 × litres. What is the cost for 8 litres?

Hint: Use the rule: Cost = rate × litres

3. Interpreting the "Story"

Interpreting graphs is a common task in exams. Here are key aspects to focus on:

Identify Trends

Look for whether the graph is increasing or decreasing.

Find Values

Locate x value, move up to the line, then across to y-axis.

Break-even Point

Where two lines intersect, costs of two options are equal.

Maximum and Minimum

Identify highest or lowest points on the graph.

Test Yourself: Interpreting Graphs

3 Questions

1 On a distance-time graph, a flat horizontal section means:

Moving fast

Stopped/stationary

Returning to start

Accelerating

2 The point where two lines cross is called the:

Starting point

End point

Break-even point

Origin

3 A steep line on a graph indicates:

Slow rate of change

Fast rate of change

No change

Negative change

0/3

4. Common South African Contexts

Cell Phone Contracts

Pre-paid graphs start at 0, while Contract graphs begin higher due to a fixed monthly fee.

Travel

Distance-time graphs visualize travel scenarios. A flat section indicates the vehicle has stopped.

Water/Electricity Tariffs

Step graphs show how the price per unit increases with higher usage.

Cell Phone Contract Comparison

Minutes Used	0	50	100	150
Pre-paid (R)	0	100	200	300
Contract (R)	100	150	200	250

Break-even point: At 100 minutes, both options cost R200.

Exam Tip: In Paper 2 of the exam, you may be presented with a graph and asked to describe its movement. Pay attention to the steepness of the line: a steep line indicates a fast rate of change, while a flatter line suggests a slower rate of change.

Test Yourself: SA Contexts

3 Questions

1 A pre-paid cell phone graph starts at:

0 (origin)

R100

Negative value

Depends on usage

2 On a distance-time graph, a flat section means:

The vehicle is moving fast

The vehicle has stopped

The vehicle is returning

The vehicle is speeding

3 Water and electricity tariffs often use which type of graph?

Linear graphs

Step graphs

Inverse curves

Horizontal lines

0/3

Final Assessment: Graphs

8 Questions

1 A graph showing a fixed monthly fee of R200 is a:

Linear graph

Horizontal line

Inverse curve

Step graph

2 The independent variable is always placed on which axis?

x-axis (horizontal)

y-axis (vertical)

Both axes

Neither

3 A graph showing the number of cars (cannot have half a car) should be:

Continuous (solid line)

Discrete (points/dotted)

Linear

Inverse

4 On a distance-time graph, what does a steep upward line mean?

Slow speed

Fast speed

Stopped

Returning

5 The point where two lines cross on a graph showing two options is called:

Starting point

End point

Break-even point

Origin

6 A contract cell phone graph starts higher than pre-paid because of:

Variable costs

Fixed monthly fee

Free minutes

Tax

7 Water tariffs that increase in steps are shown as:

Linear graph

Step graph

Inverse curve

Horizontal line

8 A flat line on a graph indicates:

Increase

Decrease

No change

Fast change

0/8

Conclusion

By familiarizing yourself with these concepts and practicing graph interpretation, you will be well-prepared to tackle graph-related questions in your Mathematical Literacy assessments.