To find the slope you need to differentiate the equation:
f(X)=7X-2X^2
dY/dX = 7 - 2x2X^1 = 7 - 4X
Now find what dY/dX equals at the point (-1,-9):
So, X=-1, dY/dX = 7 - (4x-1) = 7 + 4 = 11
Then the equation of a tangent can be written as:
Y - b = m(X - a)
where m = dY/dX , and (a,b) is the point on the tangent, i.e. (-1, -9)
So the equation of the tangent is:
Y - (-9) = 11(X - (-1))
Y + 9 = 11(X + 1)
Y + 9 = 11X + 11
Y = 11X + 11 - 9
Y = 11X + 2