Question

y ≥ 2x + 2
which of the following graphs represents the solution set of the inequality above?
graphs labeled w, x, y, z are shown (omitted here as per ocr instructions)

Explanation:

Step1: Analyze the inequality type

The inequality is \( y \geq 2x + 2 \). For a linear inequality \( y \geq mx + b \), the boundary line is solid (because of the "greater than or equal to" sign, \( \geq \)) and we shade above the line.

Step2: Check the boundary line

The equation of the boundary line is \( y = 2x + 2 \). The slope \( m = 2 \) and the y - intercept \( b = 2 \). So the line should cross the y - axis at \( (0,2) \) and have a positive slope.

Step3: Check the shading and line type

• For graph W: The line is solid (correct for \( \geq \)), it has a slope of 2 and y - intercept at 2, and the shading is above the line (correct for \( y \geq 2x + 2 \)).
• For graph X: The line has a different slope (not 2) and the shading direction seems incorrect.
• For graph Y: The line is dashed (incorrect, should be solid for \( \geq \)).
• For graph Z: The line is dashed (incorrect, should be solid for \( \geq \)).

Answer:

W.