Final answer:
The equation of the line passing through the points (-6,9) and (0,-9) is y = 3x + 27.
Step-by-step explanation:
To find the equation of the line passing through the points (-6,9) and (0,-9), we can use the point-slope form of a line: y - y1 = m(x - x1). Here, the slope (m) can be calculated as (change in y / change in x), which is (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we have:
y - 9 = (9 - (-9)) / (-6 - 0)(x - (-6))
y - 9 = 3x +18
y = 3x + 27
Therefore, the equation of the line is y = 3x + 27.