4
algebra

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

A

y≤−x+2y \leq -x + 2

B

y<−x+2y < -x + 2

C

y≥−x+2y \geq -x + 2

D

y≤x+2y \leq x + 2

Correct Answer: A

Choice A is the correct answer. Find the line equation and inequality type.

  1. Slope: m=0−22−0=−1m = \frac{0-2}{2-0} = -1
  2. Y-intercept: b=2b = 2
  3. Equation: y=−x+2y = -x + 2
  4. Type: Solid line →≤\rightarrow \leq or ≥\geq
  5. Shading: Below →≤\rightarrow \leq
  6. Result: y≤−x+2y \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.

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Linear Functions Set 73