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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

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

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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