Write the equation of the line that is perpendicular to $y=-2 x+1$ and passes through $(4,-2)$

Step 1 ：The slope of the given line is -2.

Step 2 ：The slope of a line perpendicular to this line would be the negative reciprocal of -2, which is 1/2.

Step 3 ：The equation of a line is given by \(y = mx + c\), where m is the slope and c is the y-intercept.

Step 4 ：We know the slope (m) and a point on the line (4,-2), so we can substitute these values into the equation to find the y-intercept (c).

Step 5 ：After substituting, we get m = 0.5 and c = -4.0.

Step 6 ：\(\boxed{y = \frac{1}{2}x - 4}\) is the equation of the line.