2026-08-29T20:03:52.779044 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL The graph shows the fare charged by a taxi firm, ...
Question 1 Report
The graph shows the fare charged by a taxi firm, in pounds, plotted against the distance travelled, in miles, for journeys up to 10 miles.
Use the graph to work out the fare for a journey of 5 miles. (2)Answer Details
This question tests reading an exact value from a straight-line conversion graph. Since the graph is linear, every 1 mile increase in distance adds the same fixed amount to the fare, so the value at \(d=5\) can be read directly from the drawn line.
Locating \(d=5\) miles on the horizontal axis, tracing vertically up to the plotted line, and then tracing horizontally across to the fare axis gives a reading of \(£10.80\):
The correct fare for a \(5\) mile journey is \(£10.80\) [2 marks], with one mark typically available for showing a construction line up to the graph at \(d=5\) and one for the correct reading (a small tolerance either side of \(£10.80\) is usually accepted, since it comes from a graph).
Because the graph is a straight line, this reading is consistent with a fare formula of the form \(F = a + bd\): the line meets the fare axis at \(d=0\) at about \(£2.80\) (a fixed charge) and rises by about \(£1.60\) for every extra mile, so \(£2.80 + 1.60 \times 5 = £10.80\) agrees exactly with the graph reading.
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