Final answer:
To find the equation of a perpendicular line, find the slope of the given line, determine the negative reciprocal of the slope, and use a point-slope form of a line to form the equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line, we first need to find the slope of the given line. The slope of a line can be found using the formula ∆y/∆x, where ∆y is the change in the y-coordinates and ∆x is the change in the x-coordinates.
Given that the line passes through the points (5,9) and (3,-15), the slope of the given line is (-15-9)/(3-5) = -12/-2 = 6.
A line that is perpendicular to a given line has a slope that is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is -1/6.
Using the point-slope form of a line, y-y1 = m(x-x1), where (x1, y1) is a point on the line and m is the slope, we can use the point (2,3) and the slope -1/6 to find the equation of the perpendicular line as y-3 = -(1/6)(x-2).