Final answer:
No, the lines y = 1/2x + 2 and y = 2x + 7 are not perpendicular.
Step-by-step explanation:
Two lines are perpendicular if the product of their slopes is -1. The slope of the first line, y = 1/2x + 2, is 1/2. The slope of the second line, y = 2x + 7, is 2. Multiplying the slopes: (1/2)(2) = 1, which is not -1. Therefore, the lines y = 1/2x + 2 and y = 2x + 7 are not perpendicular.
Two lines are perpendicular if the product of their slopes is -1. The slope of the line given by the equation y = ½x is ½, and the slope of the line given by y = 2x + 7 is 2. Multiplying these slopes together, ½ × 2 = 1, which is not -1. Therefore, the lines represented by these equations are not perpendicular.