Maths: line graphs

A free preview from the Athena Learning Library — the same lesson registered students learn from.

In this lesson: Read values and changes from a line graph, including values between points.

Before you start

Think of a sunny day that keeps getting warmer, then cools down towards evening. If that day's temperature were drawn as a line on a graph, what would the line do — and what would a flat part of the line mean?

Watch it happen

Watch a line graph being drawn

Line graph of the distance of a walk from home: 0: 4, 10: 2, 20: 6, 30: 11, 40: 9, 50: 14, 60: 11. The points are plotted one at a time.

The axes first: minutes run along the bottom, and the vertical axis measures the distance (metres). The first point is plotted at 0 minutes, where the value is 4.

Step 1 of 7

One point, read both ways

Line graph of the distance of a walk from home: 0: 4, 10: 2, 20: 6, 30: 11, 40: 9, 50: 14, 60: 11. The highest point is ringed, with dashed lines down to the time axis and across to the value axis.

The ringed point is the highest on the graph. Drop straight down from it to read when it happened (50 minutes); go straight across to read how big it was (14). Every point on a line graph is read in those two directions.

Your turn: find the highest point

Move the ring along the line, one point at a time, until it sits on the highest point of the graph.

Line graph of the distance of a walk from home: 0: 4, 10: 2, 20: 6, 30: 11, 40: 9, 50: 14, 60: 11. A ring marks one point of the line.

Your target:

The idea

A line graph shows how something changes over time — temperature through the day is the classic example. Points are plotted at each measurement, then joined by straight lines.

To read a value, go up from the time on the horizontal axis to the line, then across to the vertical axis. Between two plotted points the line gives the best estimate for times in between.

Questions about change ask for a difference: read the start value and the end value, then subtract. A rising line means the value is increasing; the steeper the line, the faster the change.

Worked example

The line graph shows the temperature in a classroom. By how much did the value change between 8 hour and 9 hour?

Line graph of the temperature in a classroom: 8: 5, 9: 10, 10: 15, 11: 12, 12: 13, 13: 14, 14: 13, 15: 15, 16: 17.

Sort the axes first: across is time (hour), up is temperature (°c). A line graph shows how something changes — you always read TWO points and compare them.
At 8 hour, drop straight down from the point to the axis, then across: the value is 5.
At 9 hour the value is 10. The change is 10 − 5 = 5 — the value rose by 5.

Answer: It rose by 5 — from 5 to 10.

Try one yourself

On this graph of the water in a tank, at what time (hour) was the value highest, and what was it?

Line graph of the water in a tank: 0: 2, 1: 3, 2: 8, 3: 5, 4: 3, 5: 7, 6: 4, 7: 1, 8: 2.

Watch out

Reading the axes the wrong way round — time always goes along the bottom.
Giving the end temperature when the question asks how much it changed.
Assuming the value stays flat between plotted points instead of following the line.

Quick check

Try these on your own first — then reveal each answer.

1. On this graph, what is the value at 30 minute?

Line graph of the distance of a walk from home: 0: 4, 10: 6, 20: 10, 30: 11, 40: 9, 50: 7, 60: 6.

2. On this graph, how much did the value change between 8 hour and 16 hour?

Line graph of the temperature in a classroom: 8: 4, 9: 8, 10: 9, 11: 12, 12: 10, 13: 8, 14: 7, 15: 7, 16: 7.

Practise this concept

Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.

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