Questions and Answers
What is the slope of a ski run that rises 5 feet for every horizontal change of 20 feet?
1/4
What is the constant rate of change between the number of hours (2, 4, 6, 8) and snowfall (3, 6, 9, 12)?
3/2
What is the slope of the line that passes through the points E(5, 1) and F(2, -7)?
8/3
If 3 pounds of peanuts cost $6.30, what is the cost of 4.5 pounds?
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What are the slope and y-intercepts for the graph of the line with points (0, 1) and (1, -1)?
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What are the slope and y-intercepts for the graph of the equation y-3=-1?
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What are the x and y intercepts for the graph of the equation 4x-3y=-12?
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Which store has rulers that cost more, Store A or Store B?
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What is the equation in slope-intercept form for the line that passes through the points (1, -3) and (-2, -3)?
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What is the solution of the system of equations y+2x=2 and y+4x=0?
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If Georgia rents 13 boats for 53 people, how many rowboats seating 3 and 5 does she rent?
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What do the slope and y-intercept represent in the equation y=4x+15 for saving money?
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What is the solution of the system by graphing y=3x+4 and y=x+2?
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Study Notes
Slope and Rate of Change
- The slope of a ski run that rises 5 feet for a horizontal change of 20 feet is 1/4.
- The constant rate of change for hours (x: 2, 4, 6, 8) and snowfall (y: 3, 6, 9, 12) is 3/2.
Line Equations and Intercepts
- The slope of the line passing through points E(5,1) and F(2,-7) is 8/3.
- For the graph passing through points (0,1) and (1,-1), the slope-intercept form is y = -2x + 1.
- The equation of the graph 4x - 3y = -12 has x-intercept at -3 and y-intercept at 4.
Real-World Applications
- If 3 pounds of peanuts cost $6.30, then the cost for 4.5 pounds is $9.45, indicating a direct variation.
- At store A, the cost of rulers is represented by y = 0.95x, which is higher than the given costs for store B (5 rulers: $4.60, 10 rulers: $9.20, etc.).
Solutions to Systems of Equations
- The equation in slope-intercept form from points (1, -3) and (-2, -3) is y = 6x + 9.
- The solution to the system of equations y + 2x = 2 and y + 4x = 0 is (-1, 4).
Problem Solving with Variables
- For a campout with 53 people and the renting of 13 rowboats (3-seater and 5-seater), the solution is 6 boats seating 3 people and 7 boats seating 5 people.
- Homer’s savings equation is y = 4x + 15, where the slope represents the weekly savings of $4, and the y-intercept indicates he starts with $15 saved.
Graphical Solutions
- The system of equations y = 3x + 4 and y = x + 2 intersects at the point (-1, 1).
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Description
This quiz consists of flashcards designed for Form 2B mathematics students. The questions primarily focus on calculating slopes and rates of change in various contexts. It's a great way to reinforce understanding of linear relationships and basic algebraic concepts.