Math Problem Statement

The value of y is directly proportional to the value of x. When x = 512, y = 128. What is the value of y when x = 64?

Group of answer choices

32

8

16

256

Solution

Since yy is directly proportional to xx, we can express this relationship as:

y=kxy = kx

where kk is the constant of proportionality. First, we need to find kk using the given values x=512x = 512 and y=128y = 128.

128=k×512128 = k \times 512

Solving for kk:

k=128512=14=0.25k = \frac{128}{512} = \frac{1}{4} = 0.25

Now, using this constant k=0.25k = 0.25, we can find yy when x=64x = 64:

y=0.25×64=16y = 0.25 \times 64 = 16

So, the value of yy when x=64x = 64 is 16.

The correct answer is:

16

Would you like more details or have any questions? Here are five related questions:

  1. What happens to yy if xx is halved in a direct proportional relationship?
  2. How would the equation change if yy was inversely proportional to xx?
  3. What is the constant of proportionality in the context of this problem?
  4. How can you verify the proportionality relationship with different values?
  5. How does the graph of a direct proportional relationship look?

Tip: When dealing with direct proportionality, remember that as one variable increases, the other increases at a constant rate defined by the proportionality constant.

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Math Problem Analysis

Mathematical Concepts

Direct Proportionality
Algebra

Formulas

y = kx (direct proportionality formula)
k = y / x

Theorems

Direct Proportionality

Suitable Grade Level

Grades 6-8