Final answer:
The graph of the equation y = -x - 4 does not pass through the first quadrant because for x < 0, the y-values are negative.
Step-by-step explanation:
The given equation is y = -x - 4. To determine whether its graph passes through the first quadrant, we need to assess the values for x and y. In the first quadrant, both x and y values are positive.
If we substitute any positive value for x into the equation, we will obtain a negative value for y. Therefore, the graph does not pass through the first quadrant. Hence, the correct answer is option A.