Question

Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?
You cannot tell without a graph
Yes…these lines are parallel
Yes…these lines are perpendicular
Yes…these lines are not parallel
No…these lines are parallel
No…these lines are perpendicular

Answer 1

You sure?

Answer 2

No…these lines are not parallel

Answer 3

Apologies for the confusion in my previous response. Let's re-evaluate the slopes of the two lines to determine if they are parallel, perpendicular, or neither.

The slope of the line passing through the points (3, 7) and (-2, -5) is:

slope = (change in y-coordinates) / (change in x-coordinates)
= (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5

The slope of the line passing through the points (4, 8) and (10, -2) is:

slope = (change in y-coordinates) / (change in x-coordinates)
= (-2 - 8) / (10 - 4)
= -10 / 6
= -5/3

Since the slopes of the two lines (12/5 and -5/3) are not equal and not negative reciprocals of each other, we can conclude that the lines are neither parallel nor perpendicular. Therefore, the lines will intersect.

The correct answer is: No, these lines are not parallel.