IGCSE Maths / Travel and other graphs
Modelling with graphs revision notes
Edexcel International GCSE Maths (4MA1), chapter 10: Travel and other graphs, specification point 3.3b-f. Free lesson.
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Real-life graphs show how one quantity changes with another, such as how a fare changes with distance. The graph’s shape, gradient and intercept tell you what is happening and let you calculate values.
What the gradient means on a real-life graph
The gradient tells you how far the vertical value rises for a given horizontal change. On a real-life graph, it represents a rate, so its units come from the axes: vertical units divided by horizontal units. For a taxi fare, the vertical axis is cost in pounds and the horizontal axis is distance in miles.
What the intercept tells you
The intercept is where the line meets the vertical axis. It shows the amount charged before the horizontal quantity has increased. For a taxi, this is the fixed charge paid before travelling any miles. A taxi fare line that starts at £3 has a £3 fixed charge. The gradient is £2 per mile, so the cost rises by £2 for every mile travelled.
How to use a graph rule to find a cost
A graph can be used as a rule as well as a picture. For a straight-line charge, add the fixed charge to the rate multiplied by the amount of travel or time.
What the shape of a graph tells you
Read the shape before reading values. A straight line has a steady rate, while a curve shows that the rate is changing. A curve has a different steepness at each point, so there is no single gradient for the whole curve. A straight line through the origin models a steady rate with nothing charged up front. A straight line starting above the origin models a steady rate plus a fixed charge. A curve getting steeper models a growing rate, such as interest on interest. A curve flattening off models a dying rate, such as a hot drink cooling towards a limit.
How to state a gradient correctly
A gradient from a real-life graph should not be given as a bare number. Its units are found from the axis labels, with the vertical unit over the horizontal unit. For example, a gradient of 2 on a cost-in-pounds against distance-in-miles graph is £2 per mile.