through: \( (4,-2) \), parallel to \( y=-x+1 \)

To find the equation of a line that passes through the point \( (4, -2) \) and is parallel to the line \( y = -x + 1 \), we start by noting that parallel lines have the same slope. The slope of the given line \( y = -x + 1 \) is -1. Therefore, the line we are looking for will also have a slope of -1. Using the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \), we plug in the point \( (4, -2) \) and the slope -1: \[ y - (-2) = -1(x - 4) \] Simplifying this, we have: \[ y + 2 = -x + 4 \] \[ y = -x + 4 - 2 \] \[ y = -x + 2 \] So, the equation of the line that passes through \( (4, -2) \) and is parallel to \( y = -x + 1 \) is \( y = -x + 2 \).