IGCSE Additional Mathematics: Straight Line Graphs Practice Questions
Linear law reduces a non-linear relationship to the form Y = mX + c so that constants can be found from a straight line graph. Take logarithms for power and exponential laws, or divide through for simpler cases.
Topic 8 of Cambridge IGCSE Additional Mathematics 0606 tests one skill repeatedly: rearranging a relationship until it matches Y = mX + c, then saying exactly what to plot. Naming the axes is where the marks sit. The questions below cover both standard forms.
What you need to know for Straight Line Graphs
- Linear formY = mX + c, where Y and X are the quantities plotted, m is the gradient and c is the intercept on the vertical axis.
- Power lawFor y = axn, take logs of both sides: lg y = n lg x + lg a. Plot lg y against lg x, gradient n and intercept lg a.
- Exponential lawFor y = abx, take logs: lg y = x lg b + lg a. Plot lg y against x, gradient lg b and intercept lg a.
- Recovering constantsIf the intercept is lg a then a equals 10 raised to that intercept. The same applies to the gradient in an exponential law.
- Non-logarithmic rearrangementFor y = Ax2 + Bx, divide by x to get y divided by x = Ax + B. Plot y over x against x.
IGCSE Additional Mathematics Straight Line Graphs questions and answers
4 exam-style questions written to the 0606 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
The variables x and y are related by y = axn, where a and n are constants. Explain how a straight line graph can be drawn, stating what should be plotted on each axis.
Show the worked answer
- Take logarithms of both sides: lg y = lg(axn).
- Apply the product law: lg y = lg a + lg(xn).
- Apply the power law: lg y = n lg x + lg a.
- This matches Y = mX + c with Y as lg y and X as lg x. Plot lg y on the vertical axis against lg x on the horizontal. The gradient is n and the vertical intercept is lg a.
A graph of lg y against lg x is a straight line with gradient 0.5 and vertical intercept 0.6. Given that y = axn, find a and n.
Show the worked answer
- From lg y = n lg x + lg a, the gradient equals n, so n = 0.5.
- The vertical intercept equals lg a, so lg a = 0.6.
- Convert from logarithmic form: a = 100.6.
- a = 3.981, which is 3.98 to 3 significant figures.
The variables x and y are related by y = abx. Show how a straight line graph can be obtained, and state the gradient and intercept.
Show the worked answer
- Take logarithms of both sides: lg y = lg a + lg(bx).
- Apply the power law to the second term: lg(bx) = x lg b.
- So lg y = (lg b)x + lg a.
- Comparing with Y = mX + c, plot lg y against x. The gradient is lg b and the vertical intercept is lg a. Note that x is plotted directly, not lg x.
The variables are related by y = Ax2 + Bx. Explain how to obtain a straight line graph without using logarithms.
Show the worked answer
- Divide every term by x, which is valid provided x is not zero: y divided by x = Ax + B.
- This is already in the form Y = mX + c, with Y as y divided by x and X as x.
- Plot y divided by x on the vertical axis against x on the horizontal axis. The gradient is A and the vertical intercept is B.
Common mistakes in this topic
- Plotting the original variables instead of the transformed ones.
- Confusing which axis takes lg x and which takes x.
- Reporting the intercept as the constant rather than its logarithm.
- Using logarithms when a simple division would do.
- Reading the gradient from two plotted points rather than from the line of best fit.
Exam tips
- Write out the transformed equation fully before saying what to plot. The rearrangement carries the marks.
- Power law means logs on both axes. Exponential law means log on the vertical axis only.
- Always convert an intercept back: if it equals lg a, then a is 10 to that power.
- Take gradient readings from the drawn line, using two widely separated points.
- Check whether the unknown is an index or a base before deciding to use logs.
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Straight Line Graphs FAQs
What is linear law?
Linear law is the technique of rearranging a non-linear relationship into the form Y equals mX plus c, so that plotting the transformed variables produces a straight line. The gradient and intercept of that line then give the unknown constants.
When do I plot lg y against lg x, and when against x?
For a power law such as y equals a times x to the power n, take logs of both sides and plot lg y against lg x. For an exponential law such as y equals a times b to the power x, plot lg y against x, because the variable is in the index.
How do I recover the constants from the graph?
Compare your transformed equation with Y equals mX plus c. If the intercept equals lg a, then a is 10 raised to the intercept value. If the gradient equals lg b, then b is 10 raised to the gradient. A gradient that equals n directly needs no conversion.
Do I always need logarithms for linear law?
No. Logarithms are needed only when an unknown constant appears as an index or a base. A relationship such as y equals Ax squared plus Bx becomes linear simply by dividing through by x, giving y over x plotted against x.
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Written to the published Cambridge IGCSE Additional Mathematics (0606) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.