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Linear Patterns and Graphs

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Linear Patterns and Graphs worksheet preview

Linear Patterns and Graphs

Linear patterns and coordinate plane illustration

📊 Part 1: Patterns and Tables

1. Look at this pattern: Triangle has 3 sides, Square has 4 sides, Pentagon has 5 sides, Hexagon has 6 sides. Complete the table and write the expression.

Table:

Shape Number (x): 3, 4, 5, 6, 7

Number of Sides (y): 3, 4, 5, 6, ____

Expression: y = ____________

2. Maya saves $5 each week. Complete the table showing her total savings.

Week (x): 1, 2, 3, 4, 5

Total Savings (y): $5, $10, ____, ____, ____

Expression: y = ____________

3. Using the table below, find the missing values:

x: 2, 4, 6, 8, 10

y: 7, 11, 15, ____, ____

What is the pattern? y increases by ____ each time x increases by 2.

4. Circle the patterns that are LINEAR:

y = 3x + 2

y = x²

y = 2x - 1

y = x × x

📈 Part 2: Graphing and Analysis

5. Plot these points on a coordinate plane and connect them: (1,4), (2,6), (3,8), (4,10)

Label your axes: x-axis: ____________, y-axis: ____________

Graph title: ________________________________

6. From your graph in question 5:

a) What is the rate of change? ______ (How much y increases for each increase of 1 in x)

b) What is the y-intercept? ______ (Where the line crosses the y-axis)

c) Write the equation: y = ______x + ______

7. A taxi charges $3 to start plus $2 per kilometre. Complete the table:

Distance (km): 0, 1, 2, 3, 4

Total Cost ($): ____, ____, ____, ____, ____

What does the $3 represent on a graph?

The slope

The y-intercept

The x-intercept

🧮 Part 3: Real-World Applications

8. A plant is 15 cm tall and grows 3 cm each week.

a) Write an expression for the plant's height after x weeks: h = ____________

b) How tall will it be after 6 weeks? ______ cm

c) After how many weeks will it be 30 cm tall? ______ weeks

9. The temperature decreases by 2°C every hour. At 3:00 PM it was 20°C.

a) Complete the table:

Time: 3 PM, 4 PM, 5 PM, 6 PM, 7 PM

Temperature (°C): 20, ____, ____, ____, ____

b) What will the temperature be at 9 PM? ______ °C

10. Look at this relationship: A gym membership costs $30 per month plus a $50 joining fee.

a) What is the rate of change? ______ per month

b) What is the starting value (y-intercept)? $ ______

c) Write the equation: Cost = ______x + ______ (where x = number of months)

11. Explain what makes a pattern linear:

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