Set 8: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Define the three boundary lines. 1. Bottom edge: The x-axis ($y=0$). Shading is above, so $y \geq 0$. 2. Left edge: The y-axis ($x=0$). Shading is right, so $x \geq 0$. 3. Hypotenuse: Line connecting $(4,0)$ and $(0,4)$. Slope is -1, y-intercept is 4. Equation: $y = -x + 4$. Shading is below, so $y \leq -x + 4$. 4. Combine: $x \geq 0, y \geq 0, y \leq -x + 4$ Strategic Tip: For triangles in the first quadrant, you usually need $x \geq 0$ and $y \geq 0$ plus one diagonal line. Choice B is incorrect because it shades above the hypotenuse. Choice C is incorrect because $x \leq 4$ and $y \leq 4$ create a square, not a triangle. Choice D is incorrect because it uses strict inequalities (dashed lines).