The equation of a line in the two-dimensional plane is normally of the form y = mx + b, where 'm' is the slope of the line and 'b' is the y-intercept. The slope of the line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1). The y-intercept 'b' of a line passing through the points (x, y) and having the slope 'm' is given by the formula y - mx.
Given two points (–p, –q) and (p, q), we can treat –p and –q as x1 and y1, and p and q as x2 and y2 respectively. Substituting these values into the slope formula, we obtain (q - -q) / (p - -p) = (q + q) / (p + p) = 2q / 2p = q / p = 1 (let's assume that p ≠ 0).
So, the slope 'm' of the line passing through (–p, –q) and (p, q) is 1.
For the y-intercept 'b', we know that the line passes through the origin (0,0) because (–p, –q) and (p, q) are symmetric about the origin. So, 'b' is just 0 - 1 * 0 = 0.
Therefore, the equation of the line that passes through the points (–p, –q) and (p, q) is y = 1x + 0 which simplifies to y = x.
Looking at the options given, 'y = x' is not one of them. Hence, the correct answer is d) None of the above.