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Linear Relationships Exploration

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Linear Relationships Exploration worksheet preview

Linear Relationships Exploration

Graph with linear line and data points

📊 Part 1: Analyzing the Pattern

Context: A local farmer sells baskets of strawberries. On Day 1, she sells 3 baskets. Each day afterward, she sells 2 more baskets than the day before.

1. Complete the table showing how many baskets are sold each day:

Day 1: 3 baskets

Day 2: _______ baskets

Day 3: _______ baskets

Day 4: _______ baskets

Day 5: _______ baskets

2. What pattern do you notice in the number of baskets sold each day?
3. How many baskets would be sold on Day 10? Show your thinking.
4. Which statement best describes this relationship?

The number of baskets increases by 3 each day

The number of baskets increases by 2 each day

The number of baskets doubles each day

The number of baskets stays the same each day

📈 Part 2: Graphs and Equations

5. Use the grid below to plot the points from your table (Day, Number of Baskets):
6. What do you notice about the shape of the graph when you connect the points?

It forms a straight line

It forms a curved line

It forms a zigzag pattern

The points don't connect

7. Write an equation that represents the number of baskets (B) sold on any day (d):

B = _________________________

8. Use your equation to check: Does it give you the correct number of baskets for Day 3?

🤔 Part 3: Extending Your Understanding

9. If the farmer started with 5 baskets on Day 1 and still increased by 2 baskets each day, how would your equation change?

New equation: B = _________________________

10. Compare the two situations. Check all that are true:

Both graphs would be straight lines

The second graph would be steeper

The second graph would start higher on the y-axis

Both situations increase at the same rate

11. Explain how the table, graph, and equation all show the same linear relationship in different ways:

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