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Lines in the Real World
Lines in the Real World
A plumber charges a £30 call-out fee plus £25 per hour. How do you work out any bill at a glance? Draw a straight-line graph. The y-intercept is £30 and the gradient is £25/hour. Read off the cost for any number of hours in seconds. Straight-line graphs are the most powerful modelling tool at GCSE — master them and you can answer virtually any contextual question the examiner sets.
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💡 Exam Tips for Linear Graphs Problems
- Always check your equation: substitute both original points back in to verify
- For graphical simultaneous equations: draw accurate lines and read coordinates precisely — errors in plotting will give wrong answers
- In context questions: always write units with your gradient (£/hour, km/h, etc.)
- Fixed charge vs variable cost: y-intercept = fixed charge; gradient = cost per unit
- Rearrange first: if the equation is not in y = mx + c form, rearrange before identifying m and c
- Negative gradient in context: means the quantity is decreasing (e.g. fuel tank emptying, candle burning down, value depreciating)
Now try it yourself
Quiz · Question 1 of 16
A taxi company charges a fixed fee plus an amount per mile. On a cost graph (£ against miles), what does the y-intercept represent?
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