A line that climbs, flattens, then dives isn't just maths — it's someone leaving, resting, and hurrying home. Learn to read it out loud.
Start readingOnce you know the grammar, you can read a graph out loud — "she walked away, then stopped, then rushed back" — just by looking at where the line goes.
This page is about one especially friendly kind of graph: the distance-time graph. It follows a journey, and every wiggle in the line is a moment in the story. By the end you'll read them without even thinking.
Every graph is built on two lines that cross in a corner. Each one is called an axis (say it "AK-sis") — that's just the name for a measuring line along the edge of a graph. Two of them, and you say axes (AK-seez).
So the corner where they meet — the bottom-left — is the start: time zero, and zero distance from home. As time ticks along, the line draws itself to the right. Its height at any moment answers one question: how far away am I right now?
That's the whole trick. Left-to-right is "when." Up-and-down is "how far." Keep those two ideas in your pocket and the rest is easy.
A journey is usually made of straight-ish pieces called segments. Read them one at a time, left to right, and each segment is a word in the sentence. There are really only three things a segment can do:
Line goes up → moving away from home. Distance is growing.
Line is flat → stopped. Time passes but distance doesn't change.
Line goes down → heading back. Distance is shrinking toward home.
Steeper line → faster. The bright steep line covers more distance in less time.
That last one is the secret ingredient. The steepness of a segment is called its gradient (or just "slope"), and on a distance-time graph the gradient is the speed. A gentle slope is a slow amble; a steep slope is a sprint. A flat line has zero gradient — zero speed — so you're standing still.
Put the three shapes together — up, flat, down — and shade them fast or slow, and you can tell any journey. Let's read a real one.
Here's Mara's afternoon, drawn as a distance-time graph. Read it left to right, segment by segment, and narrate what she's doing. Numbers here are just for the story — the shapes are the real lesson.
Now the reading, one segment at a time:
Read together: "Mara ambled to the park, paused for a moment, jogged a bit further, then raced all the way home." You just read a graph like a book. That's the entire skill — and it's the same skill grown-ups use to read a bank balance over a year or a heart-rate line on a fitness watch.
Look at the line. Which story does it tell? Tap a story (or use Tab and Enter). You'll get an instant thumbs-up or thumbs-down, and the right answer lights up green.
Tip: read the line in pieces. Up = away, flat = stopped, down = returning, steeper = faster.
Reading is one thing; feeling it is another. Drag the slider (or use the arrow keys, or the step buttons) to move a dot along Mara's journey. Watch the caption change as you cross from one segment to the next — climbing, resting, racing home.
Ready at the start line — 0 blocks from home.
The magic is that the grammar travels. Swap "distance from home" on the side axis for anything you can measure, and the shapes still tell the story — you just change the words.
One important note so you're never fooled: on these graphs, a flat line still means "not changing," but it does not mean "stopped moving." A flat temperature line means the warmth is holding steady, not that time has frozen. Always check what the side axis is measuring first — that word decides the whole story.
Once you notice this, graphs are everywhere: game scores, phone battery, a plant's height, the number of goals in a season. Every single one is a little story waiting to be read.
Three questions. Pick an answer and it checks you instantly. No pressure — mistakes are how the rules glue in.
Bottom = time. Side = how far (or how much). Read the side word first.
Up = away, flat = holding still, down = coming back.
Steeper slope = faster change. The gradient is the speed.