Final answer:
To find the equation that represents a line passing through (-6, 4) and (2, 0), we calculate the slope and y-intercept. The correct equation, using the slope-intercept form y = mx + b, is x + 2y = 2, which is option (a).
Step-by-step explanation:
The question is asking to choose the equation that represents a line passing through the points (-6, 4) and (2, 0). To find this, you need to calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (0 - 4) / (2 - (-6)) = -4/8 = -1/2. Now, using the slope-intercept form of a line (y = mx + b), we can plug in one of the points and the slope to solve for b, the y-intercept. After solving, we find the equation y = -1/2x + b. Using the point (2, 0), we get 0 = (-1/2)(2) + b, and therefore b = 1. The correct equation is y = -1/2x + 1, which can be rewritten as x + 2y = 2.
After calculating, it is clear that the correct equation is option (a) x + 2y = 2.