Reading Information from a Graph (Grade 12 NSC Matric Mathematical Literacy): Revision Notes

Reading Information from a Graph

Graphs are powerful visual tools that help us understand relationships between two quantities. When you encounter a graph, the key is to approach it systematically and extract the important information step by step.

Understanding graph components

Every graph has essential parts that you need to identify before reading any values.

Axes are the foundation of any graph - the horizontal line is called the x-axis and the vertical line is called the y-axis. Each axis represents a different quantity or variable.

The scale tells you what each grid square or marking represents. This is crucial information because without understanding the scale, you cannot read accurate values from the graph. Always look for scale indicators, which are often written near the axes or in annotations on the graph.

Identifying variables

Graphs show relationships between an independent variable and a dependent variable. The independent variable is the quantity that you can control or choose - it goes on the x-axis (horizontal). The dependent variable is the quantity that changes as a result of the independent variable - it goes on the y-axis (vertical).

In many real-world situations, the dependent variable depends on or is caused by changes in the independent variable. For example, when buying items, the total cost depends on how much you buy.

Reading values from graphs

Let's examine this graph showing the relationship between flour weight and cost. Here's how to read information systematically:

Step 1: Identify the scale

• On the y-axis (cost): Two blocks represent R100, so one block represents R50
• On the x-axis (weight): Two blocks represent 5 kg, so one block represents 2.5 kg

Step 2: Identify the variables

• Independent variable: Weight (kg) - this is what the customer chooses
• Dependent variable: Cost (R) - this depends on how much flour is purchased

Step 3: Find the starting point The graph starts at the origin (0,0), meaning R0 for 0 kg. This makes sense because if you buy no flour, you pay nothing.

Step 4: Read specific values From the graph, you can see that 25 kg of flour costs R500. You can verify this by following the line to where x = 25 kg and reading the corresponding y-value.

Calculating unit rates

Unit rate tells you the cost per single unit. From the graph, you can calculate:

$\text{Unit rate} = \frac{\text{Total cost}}{\text{Total quantity}}$

$\text{Unit rate} = \frac{\text{R500}}{25 \text{ kg}} = \text{R20 per kg}$

This means flour costs R20 for every kilogramme purchased.

Recognising linear relationships

This graph shows a linear relationship because it forms a straight line. This indicates direct proportion - as the weight doubles, the cost doubles too. The relationship is consistent throughout the graph.

Key features of linear relationships:

• The graph forms a straight line
• The relationship between variables is constant
• If one variable increases by a certain amount, the other increases proportionally

Worked example: reading graph values

Exam tips for graph reading

• Always read the title first to understand what the graph represents
• Check both axes labels and scales before attempting to read values
• Look for the starting point - does the graph pass through the origin?
• When reading values, use a ruler or straight edge to ensure accuracy
• Double-check your answers by using the unit rate to verify calculations

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