L5 · Reading graphs to solve problems

Learning goal

“I can analyze a graph - read values off it, find rates, compare two lines, and draw a conclusion that answers a real question.”

Rate of change — how much the output changes for each 1 unit of input (e.g. 15 km per hour); on a graph it is the steepness of the line.

Flat segment — a horizontal part of a graph: the output is not changing while the input keeps going (a stopped cyclist, a paused filling).

Conclusion — a statement that answers the question you were asked, supported by values read from the graph.

Intersection — the point where two graphs cross: both relations have the same output for the same input there.

Worked example

A plant's height is graphed: points (0 weeks, 3 cm), (1, 5), (2, 7), (3, 9), (4, 11). Step 1: Name the quantities: input = weeks, output = height in cm. Never read a graph before naming what each axis measures. Step 2: Starting value: at week 0 the plant is already 3 cm - the graph does not have to start at 0. Step 3: Rate of change: each week adds 2 cm. Rate = 2 cm per week. Step 4: Answer a question FROM the graph: "When will the plant reach 15 cm?" Extend the pattern: week 5 -> 13 cm, week 6 -> 15 cm. Conclusion: at week 6.

Check yourself — explain it

How do you find the rate of change from this graph?

Paired problem — example still visible

A puppy's mass graph passes through (0 months, 2 kg), (1, 3), (2, 4), (3, 5). What is the rate of change, and the puppy's mass at 5 months? -> 1 kg per month; 7 kg at 5 months

Faded completion — last step is yours

"A graph passes through (0, 10) and (4, 26). Output grows by ___ per unit of input" -> 4 ((26 - 10) / 4 = 4)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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