Math Problem Statement
Solution
Let's break down each of the questions based on the values provided on the cards. Here's how we can solve each question:
1. For card A, find the constant of proportionality.
Card A gives:
, .
In a direct variation, , where is the constant of proportionality. Solving for :
So, the constant of proportionality for card A is 5.5.
2. For card E, find the value of "k."
Card E gives:
, .
Again, using :
The value of for card E is -0.2.
3. Which card shows a relationship where the constant of proportionality is 64?
We need to check which card has . For this, we apply for each card:
- For Card B:
- For Card C:
Thus, Card C shows a relationship where the constant of proportionality is 64.
4. Write a direct variation equation to represent the relationship in card D.
Card D gives:
, .
Using , solve for :
Thus, the direct variation equation for card D is:
5. Write a direct variation equation to represent the relationship in card F.
Card F gives:
, .
Using , solve for :
Thus, the direct variation equation for card F is:
6. Which card can be represented by the equation ?
We need to find which card has a constant of proportionality :
- Card B gives (from earlier).
Thus, Card B is represented by the equation .
Would you like further explanation on any of the steps or details? Here are five related questions to expand on this:
- What does the constant of proportionality represent in a direct variation?
- How do you find the constant of proportionality when given multiple points?
- Can a direct variation have a negative constant of proportionality?
- How can you graph a direct variation equation?
- What happens to the graph if the constant of proportionality is a fraction?
Tip: In direct variation problems, always look for the ratio to identify the constant of proportionality, which stays the same for all points.
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Math Problem Analysis
Mathematical Concepts
Direct Variation
Proportionality
Algebra
Formulas
y = kx
k = y / x
Theorems
-
Suitable Grade Level
Grade 8