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In the coordinate plane, line n is represented by the equation y = \frac{1}{4}x + 6. Which equation...

In the coordinate plane, line n is represented by the equation y = \frac{1}{4}x + 6. Which equation represents a line perpendicular to line n that also passes through the point (1, 5)?
A. y = \frac{1}{4}x + \frac{1}{4}
B. y = \frac{1}{4}x + \frac{19}{4}
C. y = -4x + 9
D. y = -4x + 21

Answer

The slope of line n is \( \frac{1}{4} \). A line perpendicular to line n will have a slope that is the negative reciprocal, which is -4.

Using the point (1, 5) and the slope -4, we can use the point-slope form of the equation:

\( y - 5 = -4(x - 1) \)

Simplifying:

\( y - 5 = -4x + 4 \)

\( y = -4x + 9 \)

Therefore, the correct answer is C. y = -4x + 9.

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