Math Problem Statement
Solution
Let's analyze the problem step-by-step.
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Slope Calculation (Part a):
- The slope of a line is calculated by the formula:
- From the graph, we can choose two points. For example, (0, 40) and (10, 80).
- The change in (savings in dollars) is .
- The change in (time in weeks) is .
- So, the slope is:
- This means that the slope is 4.
Explanation of the Slope: In this context, the slope represents the rate at which Andre’s savings increase per week. Since the slope is 4, it indicates that Andre’s savings increase by $4 each week.
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Vertical Intercept Calculation (Part b):
- The vertical intercept is the point where the line crosses the y-axis (when ).
- From the graph, we can see that when , .
- Therefore, the vertical intercept is 40.
Explanation of the Vertical Intercept: In this context, the vertical intercept represents the initial amount of savings in Andre’s bank account. So, Andre started with $40 in his bank account at week 0.
Would you like more detailed explanations or have any specific questions?
Here are five related questions to further understand the concepts:
- How would the graph look if Andre saved $6 per week instead of $4?
- What does it mean if the slope of the line is negative in a savings context?
- How can we interpret the graph if the line is horizontal?
- If Andre started with $50 instead of $40, how would that affect the vertical intercept?
- What would be the total savings after 15 weeks if the slope remains the same?
Tip: Remember, the slope in a context like savings can be thought of as the "rate of change" or how fast something is increasing or decreasing.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope and Intercept
Rate of Change
Formulas
slope = (change in y) / (change in x)
Theorems
Slope-Intercept Form of a Line (y = mx + b)
Suitable Grade Level
Grades 6-8
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