Question

a line passes through the points (14,5) and (19,15) determine and equation for a perpendicular line that passes through the point (19,15)

Answer 1

The equation of the line thru  (14,5) and (19,15)  is found as follows:

                      15-5           5
slope = m = ----------- = ------ = -1
                       19-14         5

Thus, the slope of any line perpendicular to this first line has the slope

m = -1/1 = -1.

Then, using the point-slope form, y-15 = -1(x-19), or y -15 = -x + 19, or
y= -x + 34 (answer)