SAT Math · Linear inequalities in one or two variables · easy

Which statement is true about the graph of y ≤ 3x - 2?

Which statement is true about the graph of y≤3x−2y \leq 3x - 2?

Answer and explanation

Answer: C: The boundary line is solid, and the point (0,0) is not a solution.

The symbol ≤\leq includes equality, so points on the line y=3x−2y = 3x - 2 satisfy the inequality and the boundary is drawn solid. A dashed boundary is used only for strict inequalities such as << or >>. Now test (0,0)(0,0): is 0≤3(0)−2=−20 \leq 3(0) - 2 = -2? No, since 00 is greater than −2-2. So (0,0)(0,0) is not a solution, and the graph shades the side below the line, which does not contain the origin. That makes C correct. Choices A and D claim a dashed line, which is wrong. Choice B has a solid line but wrongly says (0,0)(0,0) works.

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