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:

**Identifying the variables:**Determine the independent variable (usually plotted on the x-axis) and the dependent variable (usually plotted on the y-axis).**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.**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:

$\text{Gradient} = {\frac{y_2 - y_1}{x_2 - x_1}}$$= \frac{20°C - 15°C}{12:00 - 09:00}$$\frac{5°C }{3 \text{ hours }} = 1.67°C/hour$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.