Math Problem Statement
Solution
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1. Write the equation of each line in slope-intercept form (y = mx + b):
- From the graph labeled Line A and Line B, identify the slope (rise over run) and y-intercept of each line.
2. Find the solution to the system of equations (A):
- The solution to the system of equations is the point where Line A and Line B intersect. You can read this from the graph.
3. Show work to prove the solution is correct:
- Substitute the coordinates of the intersection point into both equations to verify that it satisfies both equations.
4. Write the equation of each line for the pizza question in slope-intercept form:
- For Restaurant A and Restaurant B, calculate the slope and y-intercept from the graph, then write the equations in the form .
5. Find the solution to the system of equations (B):
- Determine where the lines for Restaurant A and Restaurant B intersect. This represents the number of toppings and the cost where both restaurants charge the same.
6. Interpret the solution in context:
- Explain what the solution means in terms of the problem. For example, the intersection point could represent where the cost of pizza with a specific number of toppings is the same at both restaurants.
7-8. Analyze the bank account graph for Landry and Lane:
- Use the graph to answer:
- When their account balances are equal.
- When one person has more than the other, and by how much.
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Math Problem Analysis
Mathematical Concepts
Systems of Equations
Graphing Linear Equations
Slope-Intercept Form
Intersection Points
Formulas
Slope-Intercept Form: y = mx + b
Theorems
Linear Equation Solution Theorem (intersection of two lines is the solution)
Suitable Grade Level
Grades 8-10
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