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Linear Relationships Exploration
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Linear Relationships Exploration
Choose the best answer where choices are given. For written responses, explain your thinking and include units when needed.
Reading Linear Equations
1.In the equation y = 4x + 7, what are the slope and y-intercept?
- Slope 7; y-intercept 4
- Slope 4; y-intercept 7
- Slope 11; y-intercept 0
- Slope 1; y-intercept 3
2.A bike rental costs $6 per hour, plus a one-time $8 helmet fee. If x is the number of hours and y is the total cost in dollars, which equation models the cost?
- y = 8x + 6
- y = 6x + 8
- y = 14x
- y = x + 14
3.A line has a negative slope. Which way does it move as you read the graph from left to right?
- It rises
- It falls
- It stays horizontal
- It becomes vertical
4.Use y = 3x - 2 to complete the table. Find y for each listed value of x.
x = 0
x = 2
x = 4
Describing and Comparing Relationships
5.Imagine a situation modeled by y = -2x + 12, where x is time in hours and y is a quantity in liters. Describe what the slope and y-intercept mean in this situation.
6.A candle is 18 inches tall and gets 3 inches shorter each hour. Let x represent hours and y represent its height in inches. Write an equation for the candle’s height.
7.Compare y = 5x + 2 and y = 5x - 6. State one feature their graphs share and one feature that differs.
8.A line is represented by y = 3x + 4. If its equation changes to y = 7x + 4, what happens to the graph?
- The line becomes steeper, and its y-intercept stays the same
- The line becomes less steep, and its y-intercept stays the same
- The line shifts up, but its slope stays the same
- The line shifts down, but its slope stays the same
Apply the Relationship
9.A community pool charges a $12 entry fee plus $4 for each hour of swimming. Let x be the number of hours and y be the total cost in dollars. Complete the table and write an equation.
0 hours
1 hour
2 hours
3 hours
Equation
10.In your own words, explain what changes when the y-intercept in y = 2x + 3 is changed to 8, while the slope remains 2.
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