Question


(a)
Is there a proportional relationship between x and y in the equation y=2x ?

A
Yes

B
No

(b)
Explain your reasoning.

Answers

Answered by GPT-4o mini
(a) **A** Yes

(b) The equation \( y = 2x \) represents a proportional relationship because it can be rewritten in the form \( y = kx \), where \( k \) is a constant. In this case, \( k = 2 \). In a proportional relationship, as one quantity (x) changes, the other quantity (y) changes at a constant rate, which is determined by the constant \( k \). Since \( y \) is directly proportional to \( x \) with a constant ratio (2 in this case), there is indeed a proportional relationship between \( x \) and \( y \). This means that if \( x \) is doubled, \( y \) will also be doubled, and the ratio \( \frac{y}{x} \) will always equal 2 for any non-zero value of \( x \).

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