Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

GRADE 10 · ALBERTAOUTCOME RF1

L1 · Interpreting Graphs That Tell a Story

Learning goal

“I can read a graph of a real situation segment by segment, explain what each part means, decide whether the data should be connected, and describe a situation that matches a given graph.”

Relation — a pairing between two quantities (here: an input quantity and an output quantity), shown as data, a graph, or a situation.
Discrete data — data that takes separate, countable values (goals per game, students per class). Points are plotted but NOT connected.
Continuous data — data that can take any value in between (time, temperature, distance). Points ARE connected.
Turning point — a point where a graph changes direction or behaviour (starts rising, levels off, starts falling).
Worked example

Maya walks from home to school. Her graph plots distance from home (km) against time (min), and is described completely here: it starts at (0, 0), rises steadily to (10, 1.2), runs flat to (15, 1.2), then rises more steeply to (20, 2.4). Step 1: Read the axes first - time is the input, distance from home is the output. Step 2: Segment 1, (0, 0) to (10, 1.2): distance grows steadily - Maya walks at a steady speed and covers 1.2 km in 10 min. Step 3: Segment 2, flat from (10, 1.2) to (15, 1.2): time passes but distance does not change - she has stopped for 5 min (say, to talk to a friend). Step 4: Segment 3, (15, 1.2) to (20, 2.4): distance grows faster than in segment 1 (1.2 km in only 5 min) - she hurries the rest of the way and arrives at 2.4 km from home at 20 min. Say it plainly: a story graph is read left to right, one segment at a time, and every change in steepness or direction is something happening in the story.

Check yourself — explain it

The flat segment means Maya was stopped because...

Paired problem — example still visible

A graph of a kettle's temperature starts at (0 min, 20°C), rises steadily to (4, 100), then stays flat to (6, 100). What happens in the flat part? -> The water has reached boiling point (100°C) and stays at 100°C while it boils, from minute 4 to minute 6.

Faded completion — last step is yours

"A cyclist's graph rises from (0, 0) to (30, 15), then falls steadily to (50, 0). The falling part means the cyclist is ___." -> riding back toward the start (distance from start decreasing to 0 at 50 min)

Ready to practise?

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