Read a graph with its units
Connect a table, a coordinate pair and a point without being misled by axis scales.
By the end: Read an input and output from labelled axes and explain what the units mean.
Try the lab first · Read the explanation
Starting recap and optional refresher
A number line locates one number. Two labelled axes locate a pair: input first, output second.
Review substitution and arithmetic, then return hereTry a concrete example
A bike ride lasts 2 hours and covers 7 kilometres. The pair (2, 7) means time first, distance second.
Make a prediction
Before changing the rule, predict one output and write down what you expect to change. Check the table after your intervention. This prediction is practice, not an assessment attempt.
Change one thing and compare
Set the input to 2. Find the highlighted point and the matching table row. Then change the input to −1: what does a negative input mean in this mathematical model, and why might it be outside a real trip?
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Connect the experiment to the idea
Two numbers, two meanings
A graph connects an input to an output. On a trip graph, the horizontal axis might measure time in hours and the vertical axis distance in kilometres. The point (2, 7) then means that after two hours the recorded distance is seven kilometres. Reversing the numbers describes a different observation.
Read the axis names, units and tick spacing before reading a point. A movement of one centimetre on your screen is not necessarily one unit. In this lab, adjacent horizontal table entries differ by one input unit; the vertical axis covers a much larger numerical range.
From a table to a graph
The rule y = 2x + 3 gives the pairs (0, 3), (1, 5), (2, 7) and (3, 9). Locate x = 2 on the horizontal axis, then move vertically to y = 7. The highlighted point and exact table describe the same calculation.
A connected line describes the chosen mathematical rule between the table rows. It does not establish that a real measurement was collected at every point. If x counts whole parcels, fractional x may not be a meaningful action even though the rule can calculate it.
What a point does not tell you
A single point does not identify a trend, a cause or a constant speed. The point (2, 7) alone does not tell you where the trip began. To calculate a rate over an interval, compare two outputs and divide their difference by the difference in inputs.
Check your interpretation: name both units aloud, identify whether the point is an observation or a calculated value, and state the input range that makes sense. The lab’s negative inputs are valid mathematics; they need a separate interpretation in a real application.
Try a new case
A graph has time (hours) horizontally and distance (km) vertically. What does (3, 12) say?
Take the idea with you
Read an input and output from labelled axes and explain what the units mean.
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Original LearnAI mathematics lesson. All experiments run locally on the CPU. No refresher practice or AI achievement is changed by completing this lesson.