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 2 ... for that to happen, k has to be 5 ... because 7 - 5 = 2.

so ur answer is : k = 5