College Algebra CLEP Prep Practice Exam

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What is the equation of the line perpendicular to the line x - 3y = 9 that passes through the point (4,1)?

x + 3y = 12
3x - y = 25
x + 3y = 15
3x + y = 9

The correct answer is: x + 3y = 12

Explanation To find the equation of a line perpendicular to another, we need to use the fact that the product of the slopes of perpendicular lines is -1. The given line has a slope of 1/3, so the slope of the perpendicular line will be the negative inverse of 1/3, which is -3. To find the equation of a line, we need a point and a slope. Since we are given the point (4,1), we can use the point-slope formula and plug in the values of x, y, and m (slope) to find the equation. Thus, the equation of the line perpendicular to x - 3y = 9 and passing through the point (4,1) is y - 1 = -3(x - 4). Simplifying this gives us y = -3x + 13.