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Which equation represents the line that is perpendicular to y = 1/2x + 4 and passes through the point (8,5)?

A) 2x + y = 21
B) 2x - y = 11
C) -2x + y = 19
D) -2x - y = 3

User Sth
by
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1 Answer

1 vote

Final answer:

The correct equation for the line that is perpendicular to y = 1/2x + 4 and passes through the point (8,5) is 2x + y = 21, which corresponds to option A.

Step-by-step explanation:

The question asks which equation represents the line that is perpendicular to y = 1/2x + 4 and passes through the point (8,5). To find this line, we need to determine the slope of the perpendicular line. The slope of the given line is 1/2, so the slope of the perpendicular line must be the negative reciprocal, which is -2. Using the slope-intercept form y = mx + b, where m is the slope, we plug in the slope and the point through which the line passes to find the y-intercept b.

Starting with the point-slope form:

y - 5 = -2(x - 8)

Expanding, we get:

y - 5 = -2x + 16

Adding 5 to both sides gives:

y = -2x + 21

Rewriting into standard form Ax + By = C, we get:

2x + y = 21

Thus, the correct equation is option A).

User Pol
by
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