Final answer:
The slope of the line through the points (19, -2) and (-11, 10) is calculated using the slope formula as -2/5, which is not listed in the provided options.
Step-by-step explanation:
To find the slope of the line passing through the points (19, -2) and (-11, 10), we use the slope formula, which is the change in y divided by the change in x, commonly expressed as (y2 - y1) / (x2 - x1). Here, we can label our points as (x1, y1) = (19, -2) and (x2, y2) = (-11, 10).
The slope calculation would be:
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (10 - (-2)) / (-11 - 19)
Slope (m) = (10 + 2) / (-11 - 19)
Slope (m) = 12 / (-30)
Slope (m) = -2/5
Therefore, the slope of the line is -2/5, which is not one of the provided options, so there might be an error in the options or in the question itself.