Question

will the line connecting the points (0, -1) and (2,3) intersect the line passing through the points (-2,4) and (-3,3)? explain why or why not.

Answer 1

The only way that 2 lines don't intersect is when they are paralell
the only time 2 lines that are straight are paralell, is when the slopes are the same
find the slopes


slope=(y1-y2)/(x1-x2)
so the points of the line (0,-1) and (2,3) are
y1=-1
y2=3
x1=0
x2=2 so subsitute
(-1-3)/(0-2)=-4/-2=4/2=2
slope=2

the ohter one
points (-2,4) and (-3,3)
y1=4
y2=3
x1=-2
x2=-3
subsitute
(4-3)/(-2-(-3))=1/(-2+3)=1/1=1
slope=1



the slopes are different so they will intersect