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Which of the following equations describes a line passing through (6,-5) that is perpendicular to the line y = -2/3x?

A. y = 3/2x - 14
B. y = -3/2x + 7
C. y = 2/3x - 2
D. y = -2/3x - 8

User Lida
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Final answer:

The equation of a line perpendicular to y = -2/3x and passing through the point (6,-5) is y = 3/2x - 14, which corresponds to option A.

Step-by-step explanation:

The equation that represents a line perpendicular to the line y = -2/3x must have a slope that is the negative reciprocal of -2/3. The negative reciprocal of -2/3 is 3/2.

Therefore, we need to find an option with a slope of 3/2 that also passes through the point (6,-5). Using the slope-intercept form, y = mx + b, and the point (6,-5), we can substitute m with 3/2 and the coordinates of the point into the equation to find b:

y = (3/2)x + b
-5 = (3/2)(6) + b
-5 = 9 + b
b = -14

The correct equation is y = 3/2x - 14, which is option A.

User Mobilpadde
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