determine the gradient k of the straight line passing through the point (4,0) and is perpendicular to the line 4x+17y+3=0. Reply with a shortened fraction k =

Determine the gradient k of the straight line passing through the point (4,0) and is perpendicular to the line 4x+17y+3=0. Reply with a shortened fraction k = a/b

First....find the slope of the given line.....

4x + 17y + 3  = 0       get y by itself........subtract 17y from both sides

4x + 3  = -17y             divide both sides by -17

(-4/17)x - 3/17    =  y     the slope of this line is   (-4/17)

A line perpendicular to the given one will have a negative reciprocal slope =  17/4

So...if k is th gradient, we have that k = 17/4

[ The fact that this line passes thorugh (4,0)  does not affect the slope ]