7

Set 15: Linear Functions

Explanation

Answer: A

Which equation represents a line that passes through the origin and has a slope of -1?

A.

y=−xy = -x

✓ Correct
B.

y=xy = x

C.

y=−x+1y = -x + 1

D.

y=−1y = -1

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Origin means intercept is 0. 1. Intercept: Origin →b=0\rightarrow b = 0. 2. Slope: m=−1m = -1. 3. Equation: y=−1x+0→y=−xy = -1 x + 0 \rightarrow y = -x. Strategic Tip: The line y=−xy=-x is the standard diagonal line sloping downwards. Choice B is incorrect because slope is positive. Choice C is incorrect because it doesn't pass through origin. Choice D is incorrect because it is a horizontal line.

Key Steps:

•

The correct answer is y=−xy = -x

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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