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Variables and Graphs
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Variables and Graphs
📊 Part 1: Understanding Variables
1. In everyday life, one thing often changes because another thing changes. Circle the best example:
The more hours you work, the more money you earn
The colour of your shirt affects the weather
Your favourite food changes the time
2. Complete this table using the rule: y = 2x + 1
Rule: Multiply x by 2, then add 1
| x | y = 2x + 1 |
|---|---|
| 0 | _____ |
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
3. A mobile phone plan costs $30 plus $10 for each gigabyte of data. Complete the table:
| Gigabytes (x) | Total Cost ($) |
|---|---|
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
| 5 | _____ |
4. Which variable is the independent variable in the phone plan example?
Number of gigabytes
Total cost
The $30 base cost
📈 Part 2: Plotting and Interpreting Graphs
5. Using your table from Question 2 (y = 2x + 1), plot the points on the grid below:
Draw a coordinate grid and plot your points from the table. Don't forget to label your axes!
6. Look at this graph showing temperature throughout a day. Check all statements that are true:
Temperature increases during the morning
The hottest time is around midday
Temperature stays the same all day
Temperature decreases in the evening
7. Describe in your own words what happens to y when x increases by 1 in the rule y = 2x + 1:
8. A taxi charges $5 to start, then $3 for each kilometre. Write the rule for the total cost:
Total cost = ________ + ________ × number of kilometres
🎯 Part 3: Real-Life Connections
9. Give your own example of two variables where changing one affects the other:
10. Extension Challenge: Look at this table and work out the rule!
| x | y |
|---|---|
| 1 | 4 |
| 2 | 7 |
| 3 | 10 |
| 4 | 13 |
The rule is: y = ________________
11. Reflection: How might understanding variables and graphs help you in real life?
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