Math Problem Statement
Tickets to the aquarium are $11 for adults and $6 for children. An after-school program has a budget of $200 for a trip to the aquarium. Which graph represents the cost constraint in this situation if the boundary line represents the equation 11x + 6y = 200?
Solution
To determine which graph correctly represents the cost constraint , where is the number of adult tickets (costing $11 each) and is the number of child tickets (costing $6 each), we analyze the equation step by step.
Step 1: Rewrite the Equation in Slope-Intercept Form
We start with: To express in terms of , solve for : Simplify the y-intercept:
- Slope = (negative slope, meaning the line decreases)
- y-intercept = (approximately at 33 on the y-axis)
Step 2: Check Each Graph
-
Graph A:
- The line does not pass through ; the intercept is incorrect.
- Not correct.
-
Graph B:
- The line starts at and has a steeper negative slope than .
- Not correct.
-
Graph C:
- The line has a negative slope, and the intercept appears around .
- This aligns closely with the equation .
- This graph looks correct.
-
Graph D:
- The line starts at , which is too low for the correct intercept.
- Not correct.
Step 3: Final Answer
The graph that represents the equation is:
Graph C
Do you want a detailed explanation of how I verified the slope or intercept further? Let me know!
Related Questions:
- How do you graph a linear equation like step by step?
- What does the slope represent in this problem?
- How can you verify whether a point satisfies the equation ?
- How does the graph change if the budget increases to $300?
- How do you calculate the maximum number of child tickets if there are no adult tickets?
Tip:
To graph an equation efficiently, always solve for first and identify the slope and y-intercept. Then, test key points like intercepts to confirm accuracy.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Graphing Linear Equations
Formulas
Linear equation: y = mx + b
Cost constraint: 11x + 6y = 200
Theorems
Slope-Intercept Form Theorem
Suitable Grade Level
Grades 7-10