A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

y = y equals StartFraction x Over 14 squared EndFraction.
y = y equals StartFraction x Over 7 squared EndFraction.
y = 7x
y = 14x

In a direct variation, the relationship between \( x \) and \( y \) can be written as \( y = kx \), where \( k \) is the constant of variation.

To find \( k \), we use the given points \( (2, 14) \) and \( (4, 28) \).

1. Using the point \( (2, 14) \):
\[
14 = k(2)
\]
Solving for \( k \):
\[
k = \frac{14}{2} = 7
\]

So, the equation of the function is:
\[
y = 7x
\]

Thus, the correct answer is \( y = 7x \).

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:
1. What is a direct variation, and how is it different from inverse variation?
2. How do you find the constant of variation in a direct variation problem?
3. If a new point \( (6, y) \) is added to the same function, what will \( y \) be?
4. How do you interpret the slope in a direct variation function?
5. Can a direct variation function have a negative constant of variation?

**Tip:** In a direct variation, as one variable increases, the other variable increases proportionally.

This problem demonstrates how to find the equation of a direct variation function using the points (2, 14) and (4, 28). Learn how to calculate the constant of variation and write the equation of the function y = 7x. Suitable for students in Grades 7-9 studying direct variation and linear functions.

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