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).