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?
Signup and view all the answers
What are the slope and y-intercepts for the graph of the line with points (0, 1) and (1, -1)?
Signup and view all the answers
What are the slope and y-intercepts for the graph of the equation y-3=-1?
Signup and view all the answers
What are the x and y intercepts for the graph of the equation 4x-3y=-12?
Signup and view all the answers
Which store has rulers that cost more, Store A or Store B?
Signup and view all the answers
What is the equation in slope-intercept form for the line that passes through the points (1, -3) and (-2, -3)?
Signup and view all the answers
What is the solution of the system of equations y+2x=2 and y+4x=0?
Signup and view all the answers
If Georgia rents 13 boats for 53 people, how many rowboats seating 3 and 5 does she rent?
Signup and view all the answers
What do the slope and y-intercept represent in the equation y=4x+15 for saving money?
Signup and view all the answers
What is the solution of the system by graphing y=3x+4 and y=x+2?
Signup and view all the answers
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).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
