Question

Does the line passing through the points (−1,−5) and (2,1) intersect the line passing through the points (−1,−6) and (1,2)?

Answer 1

Yes

Explanation:

As long as the slopes of these two lines are not the same, they will intersect.

Given two points on a line, we can find the slope by taking the difference in the y coordinates and dividing it by the difference in the x coordinates.

Slope of 1st line:
`(-5-1)/(-1-2) =(-6)/(-3) =(1)/(2)`

Slope of 2nd line:
`(-6-2)/(-1-1) =(-8)/(-2)=4`

The slopes are not equal, therefore the lines intersect.