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Linear Relationships Exploration
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Linear Relationships Exploration
📊 Part 1: Understanding Linear Equations
1. For the equation y = 3x + 2, what is the slope (m) and y-intercept (b)?
Slope = 2, Y-intercept = 3
Slope = 3, Y-intercept = 2
Slope = 5, Y-intercept = 0
Slope = 1, Y-intercept = 5
2. A pizza delivery service charges $3 per pizza plus a $4 delivery fee. Which equation represents this situation?
y = 4x + 3
y = 3x + 4
y = 7x
y = x + 7
3. What happens to a line when the slope (m) is negative?
The line goes up from left to right
The line goes down from left to right
The line is horizontal
The line is vertical
4. Complete the table for the equation y = 2x - 1:
| x | y |
|---|---|
| 0 | _____ |
| 1 | _____ |
| 3 | _____ |
✏️ Part 2: Verbal Descriptions and Analysis
5. Write a verbal description for the equation y = -3x + 5. Explain what the slope and y-intercept mean in real-world terms.
6. A water tank starts with 50 gallons and drains at a rate of 5 gallons per hour. Write the linear equation that represents this situation.
Equation: y = ________________
7. Compare these two equations: y = 2x + 3 and y = 2x - 1. What is the same and what is different about their graphs?
8. Look at the equation y = 4x + 2. If you changed it to y = 6x + 2, how would the graph change?
The line would be steeper
The line would be less steep
The line would move up
The line would move down
🎯 Part 3: Problem Solving
9. A gym membership costs $25 to join plus $15 per month. Create a table showing the total cost for 0, 1, 2, and 3 months, then write the equation.
| Months (x) | Total Cost (y) |
|---|---|
| 0 | _____ |
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
Equation: y = ________________
10. Explain in your own words: How does changing the y-intercept (b) affect the position of a line on a graph?
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