Final answer:
To determine if two lines are parallel, their slopes must be equal. Upon calculating, the lines through (-6,-7) and (5,-6), and through (-7,6) and (-18,7) have slopes of 1/11 and -1/11, respectively, indicating that they are not parallel but perpendicular.
Step-by-step explanation:
To decide whether two lines are parallel, we need to determine if they have the same slope or gradient. The slope of a line can be calculated using the given points on the line, with the formula:
slope (m) = (y2 - y1) / (x2 - x1)
For the line through (-6,-7) and (5,-6), the slope is:
m1 = (-6 - (-7)) / (5 - (-6)) = (1) / (11)
So, m1 = 1/11.
For the line through (-7,6) and (-18,7), the slope is:
m2 = (7 - 6) / (-18 - (-7)) = (1) / (-11)
So, m2 = -1/11.
The slopes m1 and m2 are not equal, in fact they are negative reciprocals of each other, indicating that the two lines are not parallel, but instead, they are perpendicular.