Final answer:
To find the equation of a line perpendicular to y=-2x+13 passing through (6,-1), calculate the negative reciprocal of the original slope, which is 1/2, and use the point-slope form to get y = 1/2x - 4.
Step-by-step explanation:
Calculating the Equation of Perpendicular Line
To find the equation of the line perpendicular to y=-2x+13 and passing through the point (6,-1), we first need to determine the slope of the original line. The slope of any line perpendicular to it will be the negative reciprocal of the original slope. Since the slope of the given line is -2, the slope of the perpendicular line will be 1/2. Using the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point, our equation becomes y - (-1) = 1/2(x - 6). Simplifying, we get the equation in point-slope form:
y + 1 = 1/2(x - 6), which can be further simplified to y = 1/2x - 4.
Therefore, the correct answer is (c) y = 1/2x - 4.