Create and interpret line graphs (rational number axis)
Line graphs
We have seen how line graphs are ideal to see how things change over time.
As well as whole numbers, line graphs can include fractions or decimals, and this allows us to focus on things where whole numbers may not make sense.
We also look at different ways to label the axes on our graph, and how the scale may be different between the vertical axis and horizontal axis.
Plotting a graph
When we plot a line graph with decimals or fractions, we use the same approach that we use for whole numbers, but the value of each of the increments, or ticks, on the axes may be different. Once we plot the graph, we can use it to find out some useful information.
In Video 2, let's plot a line graph to see how the black puppy is growing.
We can have different scales on our vertical and horizontal axes.
Examples
QUESTION 1
The line graph below shows the height of a tree over four years.
What is the height of the tree after $2.5$2.5 years?
Does the tree grow more in the first or the second year?
The second year
AThe first year
B
QUESTION 2
A university divides its years into trimesters (one third of a year).
Roxanne is planning on enrolling at the university and uses the line graph below to see how many units of study she can complete in a given number of years.
How many years will it take Roxanne to complete $14$14 units of study?
What is the highest possible number of units of study that Roxanne can complete in $2\frac{1}{3}$213 years?
Roxanne needs to complete at least $18$18 units of study to complete her degree.
If she wants to complete her degree in the shortest amount of time, what is the highest number of units she can complete?
QUESTION 3
Luigi brings a $1.8$1.8 L bottle of water to work each day.
He records the amount of water in the bottle at the start of each hour on the line graph below.
How much water was in Luigi's bottle at the start of the day?
What time was Luigi's bottle first refilled?
$\editable{}$$\editable{}$:$\editable{}$$\editable{}$ PM
How much water did Luigi drink in the hour after first refilling his bottle?
How many hours were between the first and second time Luigi filled his bottle?
How much water did Luigi drink between the two refills?
How much did the amount of water in Luigi's bottle change between the start and end of the day?