Graphs are powerful tools for visually representing relationships between data points. This sub-section equips you with the skills to construct informative graphs from given data and interpret the information they convey.

Choosing the Right Graph Type

The first step involves selecting an appropriate graph type that effectively showcases the relationship between the variables. Here's a quick guide:

• Scatter graphs: Ideal for exploring relationships between two independent variables, where no specific order exists between the data points.
• Line graphs: Used to represent continuous data over time or another ordered sequence. They effectively depict trends and patterns.
• Bar graphs: Suitable for comparing discrete categories or quantities. Each category is represented by a bar whose height or length corresponds to the value.

Image courtesy of DataTab

Plotting Data Points

Once you've chosen the graph type, it's time to plot the data points. This involves:

1. Identifying the variables: Determine the independent variable (usually plotted on the x-axis) and the dependent variable (usually plotted on the y-axis).
2. Scaling the axes: Choose scales for both axes that ensure all data points are visible and spread out appropriately. Consider using equal scales for both axes when comparing like quantities.
3. Plotting the points: Mark each data point according to its corresponding values on the chosen axes.

Example 1:

The table below shows the distance travelled by a car at different times.

Since time is independent and distance is dependent, we'll create a line graph.

• X-axis: Labelled "Time (hours)" with a scale ranging from 0 to 3.
• Y-axis: Labelled "Distance (km)" with a scale ranging from 0 to 240 (to accommodate the largest distance).
• Plotting points: Each data point is plotted at the intersection of its corresponding time and distance values.

Interpreting the Gradient of Straight-Line Graphs

The gradient of a straight-line graph signifies the rate of change of the dependent variable with respect to the independent variable. Mathematically, it's calculated as:

• Positive gradient: Indicates that the dependent variable increases as the independent variable increases.
• Negative gradient: Indicates that the dependent variable decreases as the independent variable increases.
• Zero gradient: Represents a horizontal line, implying no change in the dependent variable with respect to the independent variable.

Example 2:

The graph created in Example 1 depicts a constant positive gradient. This signifies that the car travels at a constant speed, as the distance increases consistently with time.

Question:

The table shows the temperature (°C) recorded at different times of the day in a city.

a) Plot a line graph to represent the data.

b) Calculate the gradient of the graph between 09:00 and 12:00. Interpret the result in the context of the situation.

Solution:

a) Following the steps mentioned earlier, plot the data points on a labelled line graph with appropriate scales.

b) The gradient between 09:00 and 12:00 can be calculated as:

The positive gradient indicates that the temperature increases as time progresses between 09:00 and 12:00. The value of 1.67°C/hour signifies the rate of increase in temperature, which is approximately 1.7°C every hour.