8

Set 12: Linear Functions (Advanced)

Explanation

Answer: A

A gym membership costs $50to join and \30 per month. Which equation represents the total cost $$Cafterafterm$ months?

A.

C=30m+50C = 30m + 50

✓ Correct
B.

C=50m+30C = 50m + 30

C.

C=30m50C = 30m - 50

D.

C=80mC = 80m

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Identify the rate and starting value. 1. Rate (Slope): $30per month $$\rightarrow 30 m. 2. Start (Intercept): $50one-time fee $$\rightarrow + 50. 3. Equation: C=30m+50C = 30 m + 50. Strategic Tip: The number associated with the variable (per month, per hour) is the slope. The one-time fee is the y-intercept. Choice B is incorrect because it swaps the monthly rate and joining fee. Choice C is incorrect because it subtracts the joining fee. Choice D is incorrect because it adds the two numbers together as a single rate.

Key Steps:

The correct answer is C=30m+50C = 30m + 50

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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