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Given the equation y = 5 + 1.5x that represents the total fee, y, for visiting a tanning salon, which statement best describes the function through the points?

A. The function is a direct variation function with a constant of variation of 1.5.
B. The function is a direct variation function with a constant of variation of 1.8.
C. The function is linear but is not a direct variation function.
D. The function is not a linear function.

1 Answer

5 votes

Final answer:

The given equation y = 5 + 1.5x is a linear function with a slope of 1.5 and a y-intercept of 5, making it not a direct variation function. The correct statement that describes this function is C. The function is linear but is not a direct variation function.

Step-by-step explanation:

The given equation y = 5 + 1.5x represents the total fee, y, for visiting a tanning salon, where x is likely the number of sessions or some form of incremental service usage. This is a linear equation, which can be identified by its form y = mx + b, where m is the slope and b is the y-intercept. In this equation, the slope m is 1.5, which represents the additional fee per session or service increment, and the y-intercept b is 5, which is the initial fee regardless of the number of sessions or services used.

Based on the form of the given equation, it is not a direct variation since there is a y-intercept other than zero. A direct variation would be of the form y = kx, where k is the constant of variation and there is no y-intercept. Therefore, the correct answer to the question would be C. The function is linear but is not a direct variation function. Option A is incorrect because, although the slope is 1.5, the presence of the y-intercept means it's not a direct variation. Option B is incorrect because the slope or constant of variation is not 1.8. Lastly, Option D is incorrect as the equation is, in fact, a linear function.

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