Set 6: Linear Inequalities (Intermediate)

Explanation

Answer: A

Which inequality corresponds to the graph of a solid line passing through $(0, 2)$ and $(2, 0)$ with shading below the line?

$y \leq -x + 2$

✓ Correct

$y < -x + 2$

$y \geq -x + 2$

$y \leq x + 2$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the line equation and inequality type. 1. Slope: $m = \frac{0-2}{2-0} = -1$ 2. Y-intercept: $b = 2$ 3. Equation: $y = -x + 2$ 4. Type: Solid line $\rightarrow \leq$ or $\geq$ 5. Shading: Below $\rightarrow \leq$ 6. Result: $y \leq -x + 2$ Strategic Tip: Calculate slope first. Negative slope goes down-right. Choice B is incorrect because it uses a strict inequality (dashed line). Choice C is incorrect because it shades above. Choice D is incorrect because it has a positive slope.

Key Steps:

•

The correct answer is $y \leq -x + 2$

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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Set 6: Linear Inequalities (Intermediate)

Detailed Explanation

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