4.05 Relationships between quantities
Data in tables
When we see a table of data, often there is a relationship between the information in one column and the information in the other column. We can look for any relationships and then use this to find other values. For example, when a group of sixth-grade runners raced against third-grade runners, their times were adjusted to make it fair. Their times are written in the table below.
| ACTUAL | ADJUSTED |
|---|---|
| 35 | 43 |
| 37 | 45 |
| 48 | 56 |
| 54 | 62 |
In Video 1, we will see how to look up information in this table and calculate an adjusted time for a runner whose actual time was $40$40 secs.
Data on a graph
This time we will look at data on a graph and see how two pieces of information are related to each other. We do that by looking at the corresponding values on the vertical and horizontal axes. Let's compare your age to your sister's age and see what happens as your sister gets $1$1 year older each year. You don't have a sister? That's okay, just imagine someone else in the example.
Writing a rule
Now we can write a rule to describe one set of data to another. We identify the rule and then use variables, or letters, to write it in a shorter way. Let's write a rule using variables for our previous example that tells us how old you are based on your sister's age.
| Information | Variable |
|---|---|
| Your age | $y$y |
| Your sister's age | $x$x |
Let's see how we do this.
Writing it a different way
We looked at how to calculate your age, once we knew your sister's age. What if we wanted to write the rule in a different way? This time we will work out your sister's age if we know your age. How do you think our rule, or equation, might change?
Let's have a look in our last video.
Practice questions
Question 4
A catering company uses the following table to work out how many sandwiches are required to feed a certain number of people.
Fill in the blanks:
| Number of People | Sandwiches |
|---|---|
| $1$1 | $5$5 |
| $2$2 | $10$10 |
| $3$3 | $15$15 |
| $4$4 | $20$20 |
| $5$5 | $25$25 |
- For each person, the caterer needs to make $\editable{}$ sandwiches.
- For $6$6 people, the caterer would need to make $\editable{}$ sandwiches.
Question 5
Consider the pattern shown on this line graph:
If the pattern continues on, the next point marked on the line will be?
$\left(12,3\right)$(12,3)
A$\left(12,4\right)$(12,4)
B$\left(16,3\right)$(16,3)
CFill in the table with the points from the graph, and the one you just found (the first one is filled in for you):
$x$x-value $y$y-value $0$0 $0$0 $\editable{}$ $1$1 $8$8 $\editable{}$ $\editable{}$ $3$3 Choose the two statements that correctly describe this pattern:
The rule is $x=y\div4$x=y÷4
AThe rule is $y=4\times x$y=4×x
BThe rule is $y=x\div4$y=x÷4
CAs $x$x increases $y$y increases.
D
Question 6
Consider the pattern shown on this dot plot:
If the pattern continues on, the next point marked on the line will be $\left(\editable{},\editable{}\right)$(,).
Fill in the table with the points from the graph, and the one you just found (the first one is filled in for you):
$x$x-value $y$y-value $0$0 $0$0 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ Choose all statements that correctly describe this pattern:
The rule is $x=y\div2$x=y÷2
AThe rule is $y=x\div2$y=x÷2
BAs $x$x increases $y$y increases.
CThe rule is $y=2\times x$y=2×x
D