Final answer:
The equation for the perpendicular bisector of a line can be found using the slope-intercept form. The slope of the perpendicular bisector will be the negative reciprocal of the original slope.
Step-by-step explanation:
The equation for the perpendicular bisector of a line can be found using the slope-intercept form. To find the equation, you need the coordinates of the two points that define the line. Let's say the coordinates are (x1, y1) and (x2, y2). First, find the midpoint of the line by using the formula:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
The slope of the line can then be found using the formula:
slope = (y2 - y1) / (x2 - x1)
The slope of the perpendicular bisector will be the negative reciprocal of the original slope. Let's call this new slope 'm'. Finally, use the point-slope form of the equation to find the equation for the perpendicular bisector:
y - y1 = m(x - x1)