Final answer:
After calculating the slopes of both lines and finding that they are equal, both lines are confirmably parallel to each other.
Step-by-step explanation:
To determine if the line containing the points (-7,0) and (0,4) is parallel to the line containing the points (6,1) and (-1,-3), we need to compare their slopes. The slope of a line through two points (x1, y1) and (x2, y2) is calculated by (y2 - y1) / (x2 - x1).
For the first line, with points (-7,0) and (0,4), the slope is (4 - 0) / (0 - (-7)) = 4/7.
For the second line, with points (6,1) and (-1,-3), the slope is (-3 - 1) / (-1 - 6) = -4 / -7 = 4/7.
Since both lines have the same slope of 4/7, they are parallel to each other.