Reading Linear Graphs – Extracting Information from a Line
Once a line is already drawn, reading a linear graph means extracting useful information directly from the picture – without needing the original equation at all. Two marked points are enough to read off the gradient using the same gradient formula you already know, and the overall direction of the line tells you immediately whether the relationship is increasing, decreasing, or constant.
This is a genuinely different skill from graphing an equation: instead of starting with an equation and drawing a line, you start with a line (perhaps from a real-world dataset) and work back toward understanding what it represents.
Extracting Information from a Graph
Read the gradient from any two marked points using the gradient formula. A positive gradient means increasing, a negative gradient means decreasing, and a zero gradient means constant.
Gradient = (12 − 3) ÷ (4 − 1) = 9 ÷ 3 = 3.
A negative gradient means the line falls as x increases: decreasing.
Real-Life Application
- Distance-time graphs: reading a vehicle's speed directly from the gradient of its graph.
- Sales trends: reading whether sales are rising or falling from a graph's direction.
- Scientific data: extracting a rate of reaction from an experimental graph.
Key Takeaways
- The gradient can be read directly from any two marked points on a graph.
- A positive gradient means increasing; negative means decreasing; zero means constant.
- Reading a graph works in the opposite direction to graphing an equation.
Practice: Reading Linear Graphs
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