# Reading Off Graphs

## Reading Off Graphs Revision

**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).

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.

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

**[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

**Question 3: **The following graph can be used to convert temperature from degrees Celsius (\degreeC) to degrees Fahrenheit (\degreeF).

Use the graph to convert the following:

a) 0\degreeC to \degreeF

b) 95\degreeF to \degreeC

**[2 marks]**

a) 0\degreeC is the beginning of the scale on the horizontal axis. At this point, the temperature in Fahrenheit is 32\degreeF

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

As shown on the graph, 95\degreeF is equivalent to 35\degreeC

**Question 4: **Consider the following graph:

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

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

**[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

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