Reading graphs

A graph is a story. Learn to read it

You already draw graphs. Today the opposite skill, maybe more useful in life: from a finished graph, read what happened. Graphs jump at you everywhere — weather, game prices, view counts, a fitness app.

Reading a graph has two basic questions. “What is y for this x?” — you find x on the horizontal axis, go up vertically to the curve, then horizontally to the y-axis. “What is x for this y?” — the same path, just from the other side.

Then there are smarter questions: where the graph grows and where it falls. Where it is highest and lowest. Where it crosses an axis (the value zero). And when there are two graphs in the picture: where they cross — there both functions have the same value.

It sounds simple, and it is simple. Still, marks fall on this in entrance exams — because of rushing and unread axes. Today you will train reading slowly and exactly.

Tereza checks yesterday’s temperature graph in an app. “At six in the morning it was 8 degrees, then it grew to 19 at three in the afternoon, in the evening down again.” Jonáš looks: “And here at night the curve pushed through zero — it froze.” Tereza nods: “One picture and you read the whole day. Try telling the same story as a table hour by hour — you will fall asleep.” A graph is a packed story: who can read the axes reads it in ten seconds.

Six questions to ask a graph

1. What is on the axes? Horizontal axis x (for example time), vertical axis y (for example Kč). Without that, do not read on.

2. What is the value at a point? For x = 4: find 4 on the x-axis, go vertically to the curve, then horizontally to the y-axis. Read the number. A pencil and a ruler are not embarrassing — they are accuracy.

3. Where does the graph grow and where does it fall? Read left to right like text. The curve goes up = it grows. Down = it falls. Horizontal = it holds.

4. Where are the extremes? Highest point = maximum, lowest = minimum. In entrance exams they ask “when was there the most” — the answer is the value on the x-axis (when), not on the y-axis (how much). Read the question carefully.

5. Where does the graph cross the axes? A crossing with the x-axis means y = 0 (for example an account at zero). A crossing with the y-axis is the starting value (x = 0).

6. Where do two graphs cross? At the crossing both functions have the same x and the same y. Two tariffs cost the same, two runners are side by side. Left of the crossing one leads, right the other.

Example 1: reading off a value

Question: A graph shows saving: a line through points [0; 100] and [4; 300]. How much was saved in week 2, and when was 250 Kč saved?

Method: Question 1: x = 2 is exactly in the middle between 0 and 4, so y will be in the middle between 100 and 300, so 200 Kč. (With a straight line, halving works.)

Question 2: I look for y = 250. That is three quarters of the way from 100 to 300 — so x = 3.

Answer: In week 2 it was 200 Kč, the amount 250 Kč was in week 3. The rule would be y = 50x + 100 — substituting confirms both answers.

Example 2: when was there the most?

Question: A graph of pool visits during the day: from 6:00 it grows from 20 people, peak 180 people at 17:00, then it falls to 40 at 21:00. Questions: When were there the most people? How many? When was attendance falling?

Method: The peak of the curve is the maximum. “When” = I read on the x-axis: at 17:00. “How many” = I read on the y-axis: 180 people.

Falling: from the peak to the right, so from 17:00 to 21:00.

Answer: Most at 17:00, and that was 180 people; it fell from 17:00 to 21:00. Two different questions, two different axes — “when” is x, “how many” is y.

Example 3: the crossing of two tariffs

Question: A graph compares two mobile internet tariffs. Tariff A: y = 10x (10 Kč per GB, no monthly fee). Tariff B: y = 5x + 20 (a fee of 20 Kč and 5 Kč per GB). When do they cost the same?

Method: Crossing = the same price. I set 10x = 5x + 20, so 5x = 20, so x = 4. Price: y = 40 Kč.

Reading from the graph: the lines cross at the point [4; 40]. To the left (less than 4 GB) the lower line is A — A is better value. To the right, B is lower.

Answer: At 4 GB both cost 40 Kč; up to 4 GB A is better value, above 4 GB tariff B.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Start with ten. When it goes well, add more.

Train calculating function values — it is the same as reading off a graph, just without a picture. Write a whole number.

Practise the questions

On paper

Draw your own graph and then question it.

1. Draw the saving graph y = 30x + 60 for x = 0 to 8 (weeks). Read off the graph: how much is saved in week 5? Check by substituting.

2. From the same graph read off when 240 Kč will be saved. Check with the equation 240 = 30x + 60.

3. On the same picture add y = 60x (a friend saves faster, but from zero). Find the crossing and write what it means.

4. Invent three questions for your graph of the type “when”, “how much” and “who leads” — and answer them.

Now you 💪

1. Before reading a graph you always check the labels and ticks of both axes.
2. You tell apart questions “when” (x-axis) and “how much” (y-axis).
3. You know what the crossing of two graphs means, and you can find it by calculation too.

What to take from this lesson

• Reading a graph starts at the axes: what is on them and by how much the ticks jump.
• You read a value with a ruler: vertically to the curve, horizontally to the axis.
• You read growth and falling from left to right.
• “When” is the answer on the x-axis, “how much” on the y-axis.
• The crossing of two graphs = both functions have the same value.

© 2026 Ing. Martin Polak / AlgoRhino · Content usage terms