Verified answer

-4x - 7y = 14 → y = (-4/7)x - 2 ... so slope = -4/7

slope of perpendicular line = 7/4

so the required line passes thru (8, 12) with slope 7/4 and has the form y = mx + b

subsing stuff:

12 = (7/4) * 8 + b

12 = 14 + b

b = -2

so the required line in slope-intercept form is y = (7/4)x - 2

first discover the equation of the unique line -4x – 7y = 14 -7y = 14 + 4x y = -2 - 4/7x y = -4/7x - 2 meaning with the intention to be perpendicular the slope would desire to intersect at a ninety degree perspective. -4/7 would desire to alter into 7/4 so now you have y = 7/4x + Y in case you caricature a graph you will discover that the y intercept of the line that passes although (8. 12) with slope 7/4 is -2 your answer is: y = 7/4x - 2