Final answer:
After calculating the slope of the line through the points (11, -3) and (7, 9) and using the point-slope form, it appears none of the given options matches the resulting equation, which is 3x + y = 30.
Step-by-step explanation:
To find the equation of the line passing through the points (11, -3) and (7, 9), we need first to calculate the slope (m) of the line using the formula Δy/Δx = (y2 - y1)/(x2 - x1). The slope is (9 - (-3)) / (7 - 11) = 12/(-4) = -3. With the slope, we can then use the point-slope form of a line, y - y1 = m(x - x1), and plug in one of the given points, for instance (11, -3), resulting in y - (-3) = -3(x - 11).
Simplified, the equation becomes y + 3 = -3x + 33, which can then be written in standard form as 3x + y = 30. None of the given options, a) 2x + 5y = 5, b) -2x + 5y = 2, c) 2x - 5y = 5, or d) -2x - 5y = 2, matches this equation. Therefore, the correct answer is not listed among the options provided.