does the line through 3,7 and -2,-5 intersect with the line through 4,8 and 10,-2

Answer 1

Yes, the lines intersect. The line passing through (3,7) and (-2,-5) has a slope of (7 - (-5))/(3 - (-2)) = 12/5.

The line passing through (4,8) and (10,-2) has a slope of (8 - (-2))/(4 - 10) = 10/(-6) = -5/3.

Since the slopes are different, the lines will intersect at a single point.