Final Answer:
The line passing through points A(0,-5) and B(3,1) does not contain the point C.
Step-by-step explanation:
The key concept here is collinearity. If three points are collinear, they lie on the same straight line. In this case, points A(0,-5) and B(3,1) define a line segment AB. Since point C is not collinear with AB, it does not lie on the same line.
To further understand, consider the slope of the line AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). For AB, the slope is (1 - (-5)) / (3 - 0) = 6 / 3 = 2. Now, if point C is not on this line, it means the slope from A to C is different, indicating that C is not collinear with AB.
In conclusion, the position of C relative to the line AB is such that C does not lie on the line. This is deduced from the fact that the points A, B, and C are not collinear.