Final answer:
To find the equation of a line perpendicular to a given line and passing through a given point, we find the negative reciprocal of the slope of the given line and substitute the coordinates of the given point into the equation.
Step-by-step explanation:
To find the equation of the line perpendicular to the given line and passing through the given point, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal of a slope is the negative value of the reciprocal. Let's say the given line has the equation y = mx + b, where m is the slope. The equation of the perpendicular line would be y = (-1/m)x + b'. To find b', we substitute the coordinates of the given point into the equation and solve for b'.
Given line: ab ←→ y = mx + b
Point: (10, 15)
Using the point (10, 15) in the equation y = (-1/m)x + b', we can find the equation of the perpendicular line.