Math Test Form 2B Flashcards

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).