Graphs & Tables

Interpret and draw graphs from tables

Interpreting Graphs and Tables

Graphs and tables display relationships between two variables. A table shows input-output pairs. A graph gives a visual picture of the relationship. We can identify patterns, read values and determine rules from both.

Example

From Table to Graph

x | 1 | 2 | 3 | 4 | 5 y | 3 | 5 | 7 | 9 | 11 Rule: y = 2x + 1 Plot points (1,3), (2,5), (3,7), (4,9), (5,11). They form a straight line — this is a linear relationship.

Example

Reading Information from a Graph

From a distance-time graph: • A horizontal line means not moving (stationary). • A steep line means moving fast. • The gradient gives the speed. • Read the y-value for any x-value directly from the graph.

Note

Remember

Always label axes and include units. The independent variable (input) goes on the x-axis. The dependent variable (output) goes on the y-axis. A straight-line graph means a constant rate of change.

Key Vocabulary

LinearA relationship that forms a straight-line graph

GradientThe steepness of a line (rise/run)

AxesThe horizontal (x) and vertical (y) lines on a graph

CoordinateAn ordered pair (x, y) showing position on a graph

Input/OutputThe values put in (x) and the values that come out (y)

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Linear

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