Math Problem Statement

Solve the systems of equations and answer the questions based on the provided graphs. This includes writing equations in slope-intercept form, finding the solutions, proving correctness, and interpreting solutions in context.

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 y=mx+by = mx + b.

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