Question

proportional not proportional
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answer bank
the equation m = 12t + 8 represents the money earned, m, for babysitting t hours with extra tip.
the equation y = 2x represents the number of lenses, y, in x pairs of glasses.

Explanation:

Step1: Recall proportional relationship

A proportional relationship is of the form \( y = kx \) (where \( k \) is a constant) with no constant term (i.e., the line passes through the origin).

Step2: Analyze \( m = 12t + 8 \)

The equation \( m = 12t + 8 \) has a constant term \( 8 \), so it is not in the form \( y=kx \). Thus, it is not proportional.

Step3: Analyze \( y = 2x \)

The equation \( y = 2x \) is in the form \( y = kx \) with \( k = 2 \) and no constant term. Thus, it is proportional.

Answer:

• proportional: The equation \( y = 2x \) represents the number of lenses, \( y \), in \( x \) pairs of glasses.
• not proportional: The equation \( m = 12t + 8 \) represents the money earned, \( m \), for babysitting \( t \) hours with an extra tip.