Question

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

$y = \frac{x}{7}$

$y = 7x$

$y = 14x$

$y = \frac{x}{14}$

Explanation:

Step1: Recall direct variation formula

The formula for direct variation is \( y = kx \), where \( k \) is the constant of variation.

Step2: Calculate \( k \) using the first point \((2, 14)\)

Substitute \( x = 2 \) and \( y = 14 \) into \( y = kx \):
\( 14 = k \times 2 \)
Solve for \( k \): \( k=\frac{14}{2}=7 \).

Step3: Verify with the second point \((4, 28)\)

Substitute \( x = 4 \) and \( k = 7 \) into \( y = kx \):
\( y = 7\times4 = 28 \), which matches the given point.

Answer:

\( y = 7x \) (the second option)