Answer:
To find the perpendicular line to the line y = 1/2x + 4 that passes through the point (-8, 3), we can follow these steps:
Determine the slope of the given line. The line y = 1/2x + 4 is in slope-intercept form (y = mx + b), where the slope is m = 1/2.
Find the negative reciprocal of the slope from step 1 to obtain the slope of the perpendicular line. The negative reciprocal of 1/2 is -2, so the slope of the perpendicular line is -2.
Use the point-slope form of a line (y - y1 = m(x - x1)) and plug in the slope from step 2 and the point (-8, 3) to find the equation of the perpendicular line.
y - 3 = -2(x + 8)
Simplifying this equation gives:
y = -2x - 13
Therefore, the equation of the perpendicular line passing through (-8, 3) is y = -2x - 13.