This tool turns a non-linear relationship into a straight-line graph. You choose the model, enter your data, and it shows the transformed axes, the best-fit line and the values of the original constants.
Free tool · Additional Mathematics
Linear-law axes explorer
You are told to plot a straight line but cannot decide which quantities go on each axis.
Everything you enter stays on this device.
Who is this tool for?
It helps an Additional Mathematics student who knows the steps of Linear Law but cannot see what to place on each axis. It also helps a student checking a practice answer.
How do I use it?
- Choose the model, for example y = ax² + b.
- Type your data as one “x, y” pair per line. An example is loaded for each model.
- Press “Transform and fit”.
- Read which quantity goes on the vertical axis and which on the horizontal axis.
- Read the gradient, the intercept and the original constants a and b.
How does it work?
Each model is compared with Y = mX + c. For y = ax² + b, the tool sets Y = y and X = x², so the gradient m is a and the intercept c is b.
For y = axᵇ, it takes lg of both sides to get lg y = b lg x + lg a. Then m = b and a = 10^c. The line is fitted by least squares to your numbers.
What does a worked example look like?
Enter the model y = ax² + b with the data (1, 5), (2, 14), (3, 29), (4, 50) and (5, 77). The horizontal values become 1, 4, 9, 16 and 25.
The points lie on a straight line with gradient 3 and intercept 2. So a = 3 and b = 2, which gives y = 3x² + 2. Check the first point: 3 × 1 + 2 = 5.
What can the tool not tell you?
A good fit does not prove that the model is true or that one quantity causes the other. It cannot tell you about values outside the range you entered.
In the exam you draw the line by eye through the plotted points. Use the tool to understand the method, then practise by hand.
Where does this connect to the lessons?
Reading the constants back from the line is taught in interpreting a linearised model in its original variables. Try questions in the linear law practice.
The wider topic is in the Linear Law hub. For lessons with a teacher, see Additional Mathematics tuition and the one-hour trial class (from RM50).
Common questions
Why do I plot y against x² instead of y against x?
For y = ax² + b, the graph of y against x is a curve. Once you use x² as the horizontal quantity, the relationship becomes Y = mX + c, a straight line whose gradient is a and whose intercept is b.
Why does the tool reject some of my numbers?
Some transformations cannot be calculated. A logarithm needs a positive number, and dividing by x needs x not equal to zero. The tool names the row and the reason instead of giving a wrong result.
Does a good straight line prove my model is correct?
No. It shows the points fit that model well within the range you supplied. It does not prove the relationship is true, and it says nothing about values outside your data.
If choosing the axes is where you get stuck, a teacher can practise that step with you on questions from your own exercise book in a one-to-one lesson.
- Online one-to-one lessons for your child with an experienced teacher.
- Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
- Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.