College Math CLEP Prep Practice Exam

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What is the equation of the line that passes through (3,9) and is perpendicular to the line 4x + y = 8?

4x + y = 9
y = -4x + 9
y = 4x + 9
y = -4x - 9

The correct answer is: y = -4x - 9

A is incorrect because it is the equation of a parallel line, not a perpendicular line. The slope of the given line is -4 and the perpendicular line's slope should be the negative reciprocal, which is 1/4. Therefore, the correct equation would not have the same slope as the given line. B and C are both incorrect because they have the same slope as the given line, and as stated before, the perpendicular line's slope should be the negative reciprocal. The correct equation is D because the given point (3,9) satisfies the equation when substituted. Additionally, the slope (-4) multiplied by the slope of the perpendicular line (1/4) gives a product of -1, as it should for two perpendicular lines.