Mathematics
Linear equations and graphs
Class 8
Intermediate
About 20 min
Premium
Linear graphs and simultaneous equations: which taxi is cheaper?
Plot two taxi fares as straight lines, read them at any distance and find where they cost the same.
Core concept
A linear equation y = mx + c is a straight line; two lines meet at the solution of both equations
Topic: Linear equations and graphs
A taxi fare has a fixed fee when the meter starts and a rate for every kilometre. If the fixed fee is Rs 100 and the rate is Rs 40 per km, the fare for x km is y = 40x + 100. Plotted on a graph this is a straight line: the fixed fee (c) is where it starts on the fare axis, and the rate (m) is how steeply it rises. Two taxis give two lines. Where they cross, both fares are equal: that distance and fare satisfy both equations at once, which is the solution of the simultaneous equations.
What you will learn
- Write a fare as a linear equation y = mx + c and draw it as a straight line.
- Explain what the slope m and the intercept c mean in a real situation.
- Solve two simultaneous equations by finding where their graphs meet.
Before you start
- Plot points on a coordinate grid.
Materials
- Two taxi fare charts
Equipment
- Graph paper and a ruler
Procedure
- Drag a taxi's dot up or down the fare axis to change its fixed fee; tap − or + on its card to change the rate per km.
- Drag the dashed reader line to a distance and read both fares.
- Record a short trip where taxi A is cheaper, the distance where both cost the same, and a long trip where taxi B is cheaper.
- Give both taxis the same rate with different fees, and record what happens to the lines.
How this simulation is simplified
- Fares are charged per whole kilometre, with no waiting charges.