From the given equation, x + y = 0, we can know that the slope of the line that we are looking for is -1.
For that line to be tangent to the graph, it needs to meet the graph at only one point.
Let's think about the tangent line of the graph. The slope of that line will be the derivative of the function.
f'(x) = -1/4 x and we need that to be -1. Set -1/4 x = -1. Then x = 4. Now, plug this x value into f(x). f(4) = -2.
Now, we have x value, y value, and the slope of the line. -2 = - (4) + b thus, b = 2.
Therefore, the line that you are looking for is y = - x + 2.