Final answer:
The correct equation of the line perpendicular to y = 2x - 4 and passing through the point (4, -1) is y = (-1/2)x + 1, which has a negative reciprocal slope of -1/2, representative of perpendicular lines.
Step-by-step explanation:
The student is asking for an equation of a line that is perpendicular to a given line and passes through a specific point. The given line's equation is y = 2x - 4, which means the slope of this line is 2. For a line to be perpendicular to this, it must have a slope that is the negative reciprocal of 2, which is -1/2. Using the point-slope form, y - y1 = m(x - x1), with m as the slope and (x1, y1) as the given point (4, -1), we can find the equation of the perpendicular line.
To find the new equation, plug in the point and slope into the point-slope form to get y - (-1) = (-1/2)(x - 4), which simplifies to y + 1 = (-1/2)x + 2. Subtracting 1 from both sides gives us the final equation y = (-1/2)x + 1. Therefore, the correct equation describing the line perpendicular to y = 2x - 4 and passing through (4, -1) is y = (-1/2)x + 1, not y = -(1/2)x + 3 as mentioned in the student's question.