Math Problem Statement
Kevin graphed the linear function, y = 25 + 5x, which represents his saving plan for tickets to the Texans game. He will save $25 from his Christmas money and $5 each week, x, from his part-time job to have the amount of money, y, he needs to buy the tickets. If Kevin saved $10 each week instead of $5, combined with the $25 Christmas money, how would the graph of this new line compare to the graph of the original line?
Solution
Let’s analyze the question.
The original function is:
This represents Kevin's savings plan where he starts with $25 (y-intercept) and saves $5 per week (slope).
If Kevin saves $10 per week instead of $5, the new function will be:
Comparison:
- The slope of the new line (10) is greater than the slope of the original line (5).
- A greater slope means the new line is steeper than the original line.
Correct Answer:
D. The line for the new function would be steeper than the original line.
Would you like me to explain further or clarify?
Here are 5 related questions to expand your understanding:
- What does the slope of a linear function represent in real-world problems?
- How would the graph change if Kevin saved $2 per week instead?
- What happens if the initial $25 savings changes instead of the weekly savings?
- How do you find the intersection point of two linear equations like this?
- What does it mean for two lines to be parallel or perpendicular?
Tip: Always focus on the slope when analyzing changes in the steepness of a graph. The larger the slope, the steeper the line!
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Graphing Equations
Slope Analysis
Formulas
y = mx + b (slope-intercept form of a line)
Theorems
Slope comparison determines steepness
Suitable Grade Level
Grades 8-10