Find the value of k given that the line through (k,2) and (7,0) is perpendicular to the line y=x-28/5

Y = x - 28/5. The slope here is 1. A perpendicular line will have a negative reciprocal slope. So our perpendicular line will have a slope of -1.

slope = (y2 - y1) / (x2 - x1)
(k,2)x1 = k and y1 = 2
(7,0)...x2 = 7 and y2 = 0
sub
slope = (0 - 2) / (7 - k)
slope = -2 / ?now if we want the slope to be -1..that means the number where the question mark is has to be 2for that to happen, k has to be 5...because 7 - 5 = 2.

so ur answer is : k = 5