Question

a. Write an equation in standard form that represents the possible ways she can allocate her money. b. What are the x and y intercepts of this line? Interpret each value in the context of this problem. c. What is the slope of this line? Interpret this value in the context of this problem. Option 1: a. 2.50x + 1.50y = 45 b. x-intercept: 18, y-intercept: 30. In the context of this problem, the x-intercept represents the number of a-ride tickets Stevie can buy with $45, and the y-intercept represents the number of b-ride tickets she can buy with $45. c. The slope of the line is -1.67. In the context of this problem, the slope represents the rate of exchange between a-ride and b-ride tickets. Option 2: a. 2.50x + 1.50y = 45 b. x-intercept: 30, y-intercept: 18. In the context of this problem, the x-intercept represents the number of a-ride tickets Stevie can buy with $45, and the y-intercept represents the number of b-ride tickets she can buy with $45. c. The slope of the line is -1.67. In the context of this problem, the slope represents the rate of exchange between a-ride and b-ride tickets. Option 3: a. 2.50x + 1.50y = 45 b. x-intercept: 30, y-intercept: 18. In the context of this problem, the x-intercept represents the number of a-ride tickets Stevie can buy with $45, and the y-intercept represents the number of b-ride tickets she can buy with $45. c. The slope of the line is -0.6. In the context of this problem, the slope represents the rate of exchange between a-ride and b-ride tickets. Option 4: a. 1.50x + 2.50y = 45 b. x-intercept: 18, y-intercept: 30. In the context of this problem, the x-intercept represents the number of a-ride tickets Stevie can buy with $45, and the y-intercept represents the number of b-ride tickets she can buy with $45. c. The slope of the line is -0.6. In the context of this problem, the slope represents the rate of exchange between a-ride and b-ride tickets.

Answer 1

The problem demonstrates standard form equation, x and y intercepts, and slope in a real-life scenario of budget allocation. The standard form equation: 2.50x + 1.50y = 45 describes the possible ways Stevie can allocate her money, with x-intercept 18 and y-intercept 30 indicating the maximum a-ride or b-ride tickets she can buy. The slope -1.67 likewise represents the rate of exchange between the tickets.

Step-by-step explanation:

The subject of this question is exploring the relationship between costs and the number of items that can be bought within a budget, focusing on standard form equations, slope, and intercepts in mathematical context. The student is exploring how Stevie can allocate $45 between two sets of tickets (a-ride and b-ride), priced at $2.50 and $1.50 respectively.

The standard form equation for this problem is: 2.50x + 1.50y = 45

Where 'x' is the number of a-ride tickets and 'y' is the number of b-ride tickets. The x-intercept is 18 and the y-intercept is 30. These intercepts represent the maximum number of a-ride tickets (x-intercept) or b-ride tickets (y-intercept) Stevie can buy if she spends all her money on one type of ticket.

The slope of the line is -1.67. The slope, often called the rate of change, represents the rate at which one can trade a-ride tickets for b-ride tickets while remaining within the budget constraints.

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