Final answer:
The equation of a line that is perpendicular to line XY, which passes through the points (1, -2) and (5, -1), would have a slope that is the negative reciprocal of the slope of line XY. The slope of line XY is 1/4, so the perpendicular line would have a slope of -4. The general equation of the perpendicular line is y = -4x + b, where b is the y-intercept.
Step-by-step explanation:
To find an equation of a line that is perpendicular to line XY which passes through points (1, -2) and (5, -1), we must first calculate the slope of line XY. The slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so for line XY:
Slope of XY = (y2 - y1) / (x2 - x1) = (-1 - (-2)) / (5 - 1) = (1) / (4) = 1/4.
Two lines are perpendicular if their slopes are negative reciprocals of each other, so the slope of the line we are looking for would be the negative reciprocal of 1/4, which is -4. With the slope known, the equation can be written in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.
If we don't have a specific point through which the perpendicular line must pass, the equation can be expressed generally as:
y = -4x + b.