Maths Lab · Free lesson · 15 minutes
A line tells a story
Connect an equation, a table and a graph—and explain what changes and what stays fixed.
JSS2 · linear relationships01 · Think first
Start with a question.
A taxi charges ₦500 before it travels, then ₦150 for each kilometre. Is ₦150 the whole fare for a one-kilometre journey?
What you already know
- Multiply whole numbers
- Read a coordinate as (x, y)
- Substitute a number for a letter
02 · See it
See it · change one thing
Equation → table → graph
Change the rate or starting value. Predict what the line will do, then check.
y = 2x + 1. At x = 1, y = 3. The gradient is 2; the y-intercept is 1.
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | -3 | -1 | 1 | 3 | 5 |
A zero gradient gives a horizontal line. A negative gradient slopes down as x increases. The axes use different labelled scales: calculate gradient from coordinate changes, not the apparent angle of the line. Context decides which x-values are meaningful.
03 · Show steps · explain why
One justified step at a time.
- 1
y = 2x + 1
There are two parts: twice x, then add one. The coefficient 2 is the rate of change.
₦500 + ₦150/km × 4 km = ₦1,100
This is an authored teaching example, not a real transport quote.04 · Mistake clinic
Find the first wrong idea.
For a 4 km taxi trip: C = 150 × 4 = ₦600
Compare the correction and its reason
C = 500 + 150 × 4 = ₦1,100
The first wrong line drops the fixed charge. Test d = 0: the model still charges ₦500, so a model starting at zero cannot describe this fare.
Check: A positive intercept and a rate are different quantities. Name both before calculating.
A mistake is evidence about the next idea to repair. It is not a label for the learner.
05 · Your turn
Try first. Then use a hint.
06 · Check & reflect → next step
Understanding includes explaining.
Which can you now explain: the starting value, the rate of change, or how to check a reverse problem?
If substitution is still difficult, practise that prerequisite with a tutor. If it is secure, explain a different line using its table and intercept.
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JEM-J2-M05-001 · Phase 3B · repaired JSS2 Mathematics · Lesson 7 · Cartesian Graphs & Linear Relationships, printed p. 21
This published free lesson contains selected explanations and authored practice. Complete canonical volumes and tutor solutions remain in the protected Content Vault.