The idea in brief. A point on a line graph is read by dropping a line straight down to the time and straight across to the axis, and the dashed line between two labels is worth what sits halfway between them, so that value is worked out before the point is read.
Lesson video, with the working
Reading a line graph: totals and decreases
4 min 22 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
The line graph shows the number of cups of coffee a cafe sold on each day from Monday to Friday. How many cups of coffee did the cafe sell altogether over the five days?
from the graph, 150 cups were sold on Monday, 250 on Tuesday, 200 on Wednesday, 350 on Thursday and 300 on Friday
Tuesday = 250 cups
Wednesday = 200 cups
Thursday = 350 cups
Friday = 300 cups
total = 150 + 250 + 200 + 350 + 300 = 1250
The cafe sold 1250 cups altogether.
Ans: 1250
Example 1
The line graph shows the number of cars in a car park at each hour from 8 am to 1 pm. Between which two times did the number of cars decrease the most?
from the graph, there were 100 cars at 8 am, 250 at 9 am, 350 at 10 am, 300 at 11 am, 150 at 12 noon and 100 at 1 pm
9 am = 250 cars
10 am = 350 cars
11 am = 300 cars
12 noon = 150 cars
1 pm = 100 cars
10 am to 11 am = 350 − 300 = 50
11 am to 12 noon = 300 − 150 = 150
12 noon to 1 pm = 150 − 100 = 50
the greatest decrease is 150, from 11 am to 12 noon (the steepest line that shows a decrease)
Ans: 11 am to 12 noon
How to solve it
Work out the scale first. A dashed line halfway between labelled hundreds is 50 more than the line below.
Trace each point across to the number axis. Monday is halfway between 100 and 200, so it shows 150 cups.
Read every point before adding: 150 plus 250 plus 200 plus 350 plus 300 is 1250 cups.
For the greatest decrease, compare neighbouring readings in the direction time moves. Use only the sections that go down.
Subtract each later reading from the earlier one. The decreases are 50, 150 and 50.
Choose the greatest decrease: 150 cars, from 11 am to 12 noon.
The highest point tells us the most cars at one time. A decrease compares two readings, in the direction time moves.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its full working.
Question 1 of 12 · Basic · free to tryThe line graph shows the temperature in a garden at two-hour intervals from…The line graph shows the…
The line graph shows the temperature in a garden at two-hour intervals from 7 am to 5 pm on one day. What was the difference between the temperature at 7 am and the temperature at 1 pm?
What should my child look for when reading line graphs?
A line graph helps your child follow how a measured quantity changes.
What your child learns here
A line graph helps your child follow how a measured quantity changes. The horizontal axis often shows time, while the vertical axis shows the quantity and its unit. This subtopic applies the MOE Primary 4 outcome on reading and interpreting line graphs. Your child learns to distinguish a reading at one time from a change between two readings, and to support a comparison with values from the graph.
Read the title and both axis labels before following a plotted point across to its value on the vertical scale.
Find the value of one small gap from two labelled marks and the number of equal gaps between them, rather than counting marks as gaps.
Use two readings to calculate an increase or decrease, keeping the unit of the measured quantity in the answer.
Recognise a horizontal segment as an unchanged reading, and use the horizontal axis to find how long that segment lasts.
For two lines on the same graph, identify each line from the key before comparing their values at the time requested.
Does the answer make sense?
For an increase between two plotted readings, add your child's calculated increase to the earlier reading. It must give the later reading, and the answer must use the vertical axis unit rather than the time unit.
How to practise these questions
Basic questions compare two temperature readings or find how long a tank's water depth stays unchanged. Intermediate work compares successive falls, reads two classes' borrowing figures, combines weekly savings and finds a time from a stated fall in water level. Challenge questions use several readings to find an equal daily amount or total spending from pocket money and savings. Your child can begin by pointing to the exact readings needed and saying what each axis measures. When several days or weeks are involved, record the values in order before adding them, so no reading is omitted or included twice. If the next calculation is unclear, revisit the written working after the attempt and identify the readings used in its first line. On the free garden-temperature card, the written working compares the readings at two specified times and finds their difference. The multiple-choice questions read one day's value or test statements about a line graph at Basic, and at Intermediate find the interval with the greatest rise or the greatest fall.
Questions parents ask
Does each small square on a line graph stand for one? The labelled scale decides the value of a gap. Your child can subtract two labelled readings and divide by the number of equal gaps between them. The horizontal and vertical scales may use different steps, so a time gap and a quantity gap need separate readings.
Does the steepest part always show the greatest change? Compare numerical changes when the question asks for the greatest rise or fall. On one graph, steepness compares those changes directly only when the horizontal spans are equal. Your child should read the endpoints rather than assume that a steep short segment has the largest overall change.
What can I ask when my child says a flat line means zero? Ask where the segment sits on the vertical scale. A horizontal segment means the plotted quantity stays at that reading; it is zero only if the reading itself is zero. The two ends on the time axis show the period for which the reading is unchanged.
