Final answer:
Using the point-slope form, we derived the equation -4x - 3y = 2 from the given point (-4, -6) and slope -4/3. However, this equation does not match any of the provided answer choices, suggesting a possible error in the options or the question's setup.
Step-by-step explanation:
To determine the equation of the line that contains point A (-4, -6) and has a slope of m = -4/3, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Plugging in the values for point A and the slope we get:
y - (-6) = (-4/3)(x - (-4))
Simplifying further:
y + 6 = (-4/3)x - (16/3)
To get to the general form (Ax + By = C), let's clear the fractions by multiplying through by 3:
3y + 18 = -4x - 16
Then, we can bring all terms to one side to get the desired general form:
4x + 3y = -18 + 164x + 3y = -2
However, to match the answer choices given, which all have integer constants, let's multiply everything by a common factor to get rid of the fraction. Multiplying by -1 gives us the positive form of the equation:
-4x - 3y = 2, which is not an option provided. It seems there might be an error in the provided options or in the question's setup since none of the answer choices exactly match the equation derived from the given point and slope.