Final answer:
The y-intercept of the line perpendicular to y = -x + 1 passing through the point (4, 1) is -3.
Step-by-step explanation:
The student was asked to find the y-intercept of a line perpendicular to the line y = -x + 1 that includes the point (4, 1). First, we find the slope of the perpendicular line. Since the original line has a slope of -1 (the coefficient of x), the perpendicular line will have a slope that is the negative reciprocal, which is 1. Next, we use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, to find the equation of the perpendicular line: y - 1 = 1(x - 4). Simplifying, we get y = x - 3. The y-intercept is the y-coordinate of the point where the line crosses the y-axis (when x = 0). Setting x to 0 in the equation y = x - 3, we find the y-intercept is -3.