A line passes through the points (k, 4) and (3, -6). The line is perpendicular to the graph 5y + 4x = 8. What is the value of k?

Answer 1

solve for y to find the line's slope

5y=-4x +8

y =-4x/5 + 8/5

slope = the coefficient of the x term = -4/5

the slope also = the difference in y coordinates over the difference in x coordinates of 2 points on the line =

10/(k-3) = -4/5

cross multiply

-4k + 12 = 50

-4k = 38

k = 38/-4 = -19/2 = -9 1/2