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
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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