Set 9: Linear Functions

Explanation

Answer: A

Water boils at $212^\circ F$ ( $100^\circ C$ ) and freezes at $32^\circ F$ ( $0^\circ C$ ). Which linear equation converts Celsius ( $C$ ) to Fahrenheit ( $F$ )?

$F = \frac{9}{5}C + 32$

✓ Correct

$F = \frac{5}{9}C + 32$

$F = \frac{9}{5}C - 32$

$F = C + 32$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the line through two points. 1. Points: $(0, 32)$ and $(100, 212)$ . (Input C, Output F). 2. Slope: $\frac{212 - 32}{100 - 0} = \frac{180}{100} = \frac{9}{5} = 1.8$ . 3. Intercept: When $C=0, F=32$ . So $b=32$ . 4. Equation: $F = \frac{9}{5}C + 32$ . Strategic Tip: This is a classic conversion formula. Choice B is incorrect because slope is inverted. Choice C is incorrect because sign error. Choice D is incorrect because slope is 1.

Key Steps:

•

The correct answer is $F = \frac{9}{5}C + 32$

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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