Question

which equation represents the proportional relationship shown on the table? a $x = 4y$ b $x = 2y$ c $y = \frac{1}{4}x$ d $y = 4x$

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship is of the form \( y = kx \), where \( k \) is the constant of proportionality. We need to find \( k=\frac{y}{x} \) (assuming the table has \( x \) and \( y \) values, though the table data isn't shown, we can analyze the options).

Step2: Analyze Each Option

• Option A: \( x = 4y \) can be rewritten as \( y=\frac{1}{4}x \), but let's check the form. Wait, no—if we solve for \( y \), \( y=\frac{x}{4} \), but let's see the constant.
• Option B: \( x = 2y \) → \( y=\frac{x}{2} \), \( k=\frac{1}{2} \).
• Option C: \( y=\frac{1}{4}x \), so \( k = \frac{1}{4} \).
• Option D: \( y = 4x \), \( k = 4 \).

Wait, maybe the table (not shown here, but typical proportional tables) has values where when \( x \) increases, \( y \) increases by a factor. Let's assume a typical table: for example, if \( x = 4 \), \( y = 1 \); \( x = 8 \), \( y = 2 \), etc. Then \( \frac{y}{x}=\frac{1}{4} \), so \( y=\frac{1}{4}x \), which is Option C. Or maybe the table has \( x \) and \( y \) such that \( y \) is a quarter of \( x \). So the equation \( y=\frac{1}{4}x \) (Option C) represents the proportional relationship.

Answer:

C. \( y = \frac{1}{4}x \)