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Reading Graphs

Linear Graphs and y = mx + c

A graph that has a straight line is called a linear graph:

  • The vertical axis is the y-axis, while the horizontal axis is called the x-axis

  • The gradient, or slope, of the line is given the symbol 'm'

  • The line crosses the y-axis when x = 0 at the y-intercept, given the symbol 'c'

Calculating the gradient, or slope, of a linear graph is an important skill to master:

  • Draw a large triangle onto the line

  • Work out the coordinates of the two points where the triangle meets the line

  • Divide the change in y value by the change in x value

Calculating Gradients: Example A

A worked example where the gradient of a straight line is calculated.

Calculating Gradients: Example B

Another example of how to calculate the gradient of a line.

Drawing Tangents to a Curve [often higher tier only]

Sometimes you need to work out the slope at a particular point on a curve:

  • Carefully draw a straight line with a ruler that just touches the curve

  • Work out the gradient of this straight line in the usual way

Tangents: Example

A worked example where a tangent is used to find the gradient of a curve at a point.

Calculating the Area under a Graph

This is how to calculate the area under a line on a graph. It's simple maths: you just need to break up the shape into triangles and squares, take care with your readings and then work methodically through it.


This is a really important skill to master, especially as you may need to use it when calculating the displacement from a velocity-time graph.

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