The required graph is Graph (IV).
To graph the equation -x - 2y = 6, we can rewrite it in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept:
-x - 2y = 6
First, let's isolate the y-term:
-2y = x + 6
Divide both sides by -2 to solve for y:
y = (-1/2)x - 3
The coefficient of x (-1/2) represents the slope, and the constant term -3 represents the y-intercept.
The correct graph should be a straight line with a slope of -1/2 and passing through the point (0, -3).
Thus, the required graph is Graph (IV).
Learn more about Slope here: