4.05 Relationships between quantities
Consider the following table of values:
What needs to be added to each input to get the corresponding output?
Find the output when the input is 63.
| Input | 8 | 16 | 24 | 32 | 40 |
|---|---|---|---|---|---|
| Output | 34 | 42 | 50 | 58 | 66 |
Consider the following table of values:
What needs to be added to each input to get the corresponding output?
Find the output when the input is 176.
| Input | 44 | 54 | 64 | 74 | 84 |
|---|---|---|---|---|---|
| Output | 21 | 31 | 41 | 51 | 61 |
Consider the following table of values:
By what factor is each output bigger than the corresponding input?
Find the output when the input is 9.
| Input | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Output | 20 | 40 | 60 | 80 | 100 |
Consider the following table of values:
By what factor is each output smaller than the corresponding input?
Find the output when the input is 150.
| Input | 15 | 30 | 45 | 60 | 75 |
|---|---|---|---|---|---|
| Output | 1 | 2 | 3 | 4 | 5 |
Consider the following graph, where the points form a linear pattern:
State the coordinates of the next point in the pattern.
Complete the table of values for the pattern of points:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 3 |
Write the rule for the line that would pass through the given points.
As x increases, does the value of y increase or decrease?
Consider the following graph, where the points form a linear pattern:
State the coordinates of the next point in the pattern.
Complete the table of values for the pattern of points:
| x | 10 | 11 | 12 | 13 |
|---|---|---|---|---|
| y | 6 |
Write the rule for the line that would pass through the given points.
As x increases, does the value of y increase or decrease?
Consider the following graph, where the points form a linear pattern:
State the coordinates of the next point in the pattern.
Complete the table of values for the pattern of points:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y |
Write the rule for the line that would pass through the given points.
As x increases, does the value of y increase or decrease?
Consider the following graph, where the points form a linear pattern:
State the coordinates of the next point in the pattern.
Complete the table of values for the pattern of points:
| x | 0 | 4 | 8 | 12 |
|---|---|---|---|---|
| y |
Write the rule for the line that would pass through the given points.
As x increases, does the value of y increase or decrease?
Consider the following graph, where the points form a linear pattern:
State the coordinates of the next point in the pattern.
Complete the table of values on the right for the pattern of points:
| x | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| y |
Write the rule for the line that would pass through the given points.
As x increases, does the value of y increase or decrease?
Nadia has made the following table which shows her dad Glen's age compared to hers:
How old was Glen when Nadia was 1 year old?
What will Glen's age be when Nadia is 49 years old?
| Nadia's age | Glen's age |
|---|---|
| 1 | 24 |
| 5 | 28 |
| 10 | 33 |
| 20 | 43 |
| 30 | 53 |
James has made the following table which shows his sister Hermione's age compared to his:
How old was Hermione when James was 10 years old?
What will be Hermione's age when James is 65 years old?
| James's age | Hermione's age |
|---|---|
| 10 | 7 |
| 11 | 8 |
| 15 | 12 |
| 20 | 17 |
| 30 | 27 |
A catering company uses the following table to work out how many sandwiches are required to feed a certain number of people:
How many sandwiches the caterer needs for each person?
How many sandwiches the caterer would need to make for 6 people?
| Number of people | Number of sandwiches |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
| 5 | 25 |
A minibus company uses the following table to work out how many busses are needed for a certain number of passengers:
How many busses does the company need to provide for 10 people?
How many busses would the company need to provide for 100 people?
| Number of people | Number of busses |
|---|---|
| 10 | 1 |
| 20 | 2 |
| 30 | 3 |
| 40 | 4 |
| 50 | 5 |
Oliver was participating in a school readathon and his parents agreed to donate \$4 plus an extra dollar for every book read. The graph shows how much Oliver earned:
If Oliver reads more books, state the coordinates of the next point in the pattern.
Complete the table of values for the pattern of points:
| \text{No. Books read} | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \text{Money earned } (\$) |
If we let x be the number of books read and y be the money earned, write the rule for the line that would pass through the given points.
Consider the graph of points that shows the height of a seedling measured every day:
If the seedling continues to grow at the same rate, what will the next point marked on the graph be?
Complete the table of values on the right for the pattern of points:
| \text{Days }(x) | 10 | 11 | 12 | 13 |
|---|---|---|---|---|
| \text{Height }(y) |
If we let x be the number of days, and y be the height of seedling, write the rule for the line that would pass through the given points.
Consider the graph of points that shows the number of sides a given number of squares have:
The x-axis shows the number of squares, and the y-axis, shows the number of sides.
If the pattern continues on, what will the next point in the pattern be?
Complete the table of values on the right for the pattern of points:
| \text{Squares }(x) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \text{Sides }(y) |
Write the rule for the line that passes through the given points.