An experiment was conducted that recorded the weight of a new bar of soap after each use. The line of best fit for the data collected is y equals negative 5.6 x plus 123, where y is the weight of the bar of soap, in grams, and x is the number of times that the bar was used.

Question

Which statement describes the meaning of the y-intercept for the line of best fit equation?

Answer options with 4 options
A.
The weight of the new bar of soap was 123 grams.

B.
After 123 uses, the weight of the bar of soap was 5.6 grams.

C.
After every 123 uses, the weight of the bar of soap decreased by 5.6 grams.

D.
The weight of the bar of soap decreased by an average of 5.6 grams after each use.

Answer 1

The y-intercept of the line of best fit equation \( y = -5.6x + 123 \) represents the value of \( y \) (the weight of the bar of soap) when \( x \) (the number of uses) is 0. In this case, when \( x = 0 \), the equation gives:

\[ y = -5.6(0) + 123 = 123 \]

This means that when the bar of soap is brand new (not used at all), its weight is 123 grams.

Therefore, the correct statement describing the meaning of the y-intercept is:

A. The weight of the new bar of soap was 123 grams.