What Is An Equation Of The Line Tangent To The Curve (x^2) + 2x = 5 At The Point (-4,3)?

y? There is some y missing. But it seems reasonable to assume that your curve is the parabola with the function:
y = f(x) = x^2 + 2x - 5. Let's see.

1st question: What is the slope of the tangent in the Point P(-4 | 3) ?

The derivative f '(x) of the function f (x) tells you the slope m_t of the tangent in any point
P_0 (x_0 | y_0) with y_0 = f (x_0).

The 1st derivative of the parabola's function is
f '(x) = 2x + 2

2nd question: What is the function of the tangent in P ( -4| 3) ?

The general form of the equation of a straight line is:
y = mx + b, where m is the slope and b is the y-intercept. Thus the equation of our tangent t (x) is:
t (x) = f '(x) * x + b.
m = f ' (x_0) = -6; for x_0 = -4.

The slope of the tangent is -6. The only thing missing is b. Insert the x- and y-coordinates into the tangent function t(x):

t (x) = 3 = -6 * -4 + b
b = 24 - 3 = 21.

Thus your function is:
t (x) = y = -6x - 21

Which corresponds nicely to answer option D) in your list:
D) y + 6x = -21