Reading Off Graphs

Reading off Graphs

Being able to read off graphs is an important skill. Luckily, it is relatively simple and if you know the method it can be an easy way to collect marks in an exam.

How to Read off Graphs

Reading off graphs is a fundamental skill – it allows us to convert between values without having to perform complicated calculations. Providing the graph features a line (as opposed to individual points, such as in a scatter graph), we can perform conversions using the following three steps:

Identify the variable on one axis
Draw a straight line from the axis towards the graph
When the straight line crosses the graph, draw another line to the other axis and identify the value of the other variable

Example: Use the graph on the right to find the value of $y$ when $x=3$

Following the steps above, we need to first go to the position of $3$ on the $x$ -axis (horizontal axis).

Next, we need to draw a straight line upwards to the graph.

When we hit the line of the graph, draw a horizontal line across to the $y$ -axis (vertical axis).

As can be seen, the value on the $y$ -axis is $4.5$ , so when $x=3$ , $y=4.5$

Example: Conversion Graphs

The conversion graph on the right can be used to convert distances between miles and kilometres. Use the conversion graph to convert the following:

a) $5$ miles into kilometres

b) $10$ kilometres into miles

[2 marks]

a) Identify the position of $5$ miles on the horizontal axis. Next, draw a straight line upwards to the line of the graph, then draw a horizontal line from the graph to the vertical axis. As shown in the image on the right, $5$ miles is equivalent to $8$ kilometres.

b) Identify the position of $10$ kilometres on the vertical axis. Draw a straight line across to the line of the graph, then draw a vertical line downwards to the horizontal axis. As shown in the image on the right, $10$ km is equivalent to $6.2$ miles.

Note:

Reading off graphs is a simple skill, but make sure to read the question carefully. Students often make the mistake of reading from the wrong axis!

Reading Off Graphs Example Questions

Question 1: The conversion graph below can be used to convert between pounds (lbs) and kilograms (kg).

conversion graph lbs to kg Use the graph to convert $12$ lbs into kg.

[1 mark]

Draw a line from $12$ lbs on the vertical axis to the graph. Draw a second line down from the graph to the horizontal axis:

As shown in the graph, $12$ lbs is equivalent to $5.4$ kg.

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Question 2: Use the following graph to find the value of $y$ when $x=4$

square graph conversion question

[1 mark]

Go to the value of $x=4$ on the horizontal ( $x$ ) axis and draw a straight line up to the graph. Where the straight line meets the curve, draw a horizontal line across to the vertical ( $y$ ) axis.

As shown in the graph above, $y=1.6$ when $x=4$

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Question 3: The following graph can be used to convert temperature from degrees Celsius ( $degree$ C) to degrees Fahrenheit ( $degree$ F).

celsius to fahrenheit graph Use the graph to convert the following:

a) $0degree$ C to $degree$ F

b) $95degree$ F to $degree$ C

[2 marks]

a) $0degree$ C is the beginning of the scale on the horizontal axis. At this point, the temperature in Fahrenheit is $32degree$ F

b) Draw a horizontal line across from $95degree$ to the line of the graph. Draw a vertical line down from the graph to the horizontal axis.

As shown on the graph, $95degree$ F is equivalent to $35degree$ C

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Question 4: Consider the following graph:

cubic graph question

Use the graph to answer the following:

a) Give the value of $y$ when $x=2$

b) Give the value of $x$ when $y=6$

[2 marks]

a) Draw a vertical line up from $x=2$ to the graph. Then draw a straight line across to the $y$ -axis. When $x=2$ , $y=2$

b) Draw a horizontal line across from $y=6$ to the graph. Then draw a vertical line down to the $x$ -axis. When $y=6$ , $x=4$

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Question 5: Give the values of $x$ when $y=3$

modulus graph

[2 marks]

This graph has an unusual shape, but we can still apply the same method to read the values we need.

Go to the value of $3$ on the $y$ -axis and then draw a horizonal line across to the graph. Note that there are two points where our line will cross the graph, so we will include both. Draw a vertical line down to the $x$ -axis from these points. When $y=3$ , $x=2$ and $x=4$