Final answer:
To find the equation of a line perpendicular to y = -1/2x + 6 and passing through the point (6, -10), we need to determine the slope of the new line. Using the slope-intercept form of a line, y = mx + b, we can substitute the point (6, -10) and the slope 2 to find the equation of the line: y = 2x - 22.
Step-by-step explanation:
To find the equation of a line perpendicular to y = -1/2x + 6 and passing through the point (6, -10), we need to determine the slope of the new line. The slope of a line perpendicular to another line is the negative reciprocal of its slope. The given line has a slope of -1/2, so the new line will have a slope of 2.
Using the slope-intercept form of a line, y = mx + b, we can substitute the point (6, -10) and the slope 2 to find the equation of the line:
-10 = 2(6) + b
Solving for b, we have:
b = -10 - 2(6)
b = -10 - 12
b = -22
Therefore, the equation of the line perpendicular to y = -1/2x + 6 and passing through (6, -10) is y = 2x - 22.