Which of these represents a linear function that contains the point (-8, 3) and is perpendicular to 4x + y...

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Which of these represents a linear function that contains the point (-8, 3) and is perpendicular to 4x + y = 2? A. y = \frac{1}{4}x + 1 B. y = \frac{1}{4}x + 5 C. y = -4x + 35 D. y = -4x - 29

SnapAndSolve AI · Accepted Answer

To find the line perpendicular to 4x + y = 2, we first find the slope of this line. Rewriting in slope-intercept form (y = mx + b), we get y = -4x + 2, so the slope is -4. The perpendicular slope is the negative reciprocal, which is 1/4.

Now, we check which line with slope 1/4 passes through the point (-8, 3).

For A. y = \frac{1}{4}x + 1, substituting (-8, 3): 3 = \frac{1}{4}(-8) + 1 = -2 + 1 = -1 (not equal to 3).
For B. y = \frac{1}{4}x + 5, substituting (-8, 3): 3 = \frac{1}{4}(-8) + 5 = -2 + 5 = 3 (equal to 3).
For C. y = -4x + 35, the slope is incorrect.
For D. y = -4x - 29, the slope is incorrect.

The correct answer is B. y = \frac{1}{4}x + 5.

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Which of these represents a linear function that contains the point (-8, 3) and is perpendicular to 4x + y...

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