Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?

Yes…these lines are perpendicular

You cannot tell without a graph

Yes…these lines are not parallel

No…these lines are parallel

Yes…these lines are parallel

No…these lines are perpendicula

You cannot tell without a graph

Yes…these lines are not parallel

In order to determine if the lines intersect or not, we need to first find the slopes of the two lines.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Let's find the slopes of the two lines:

Line 1: Passing through (3, 7) and (-2, -5)
slope1 = (-5 - 7) / (-2 - 3) = -12 / -5 = 12 / 5

Line 2: Passing through (4, 8) and (10, -2)
slope2 = (-2 - 8) / (10 - 4) = -10 / 6 = -5 / 3

Now, if the slopes of the two lines are equal, they are parallel. If the product of the slopes is -1, then the two lines are perpendicular.

Let's check:

slope1 * slope2 = (12 / 5) * (-5 / 3) = -12 / 3 = -4

Since the product of the slopes is not -1, we can conclude that the two lines are parallel.

Therefore, the correct answer is: No, these lines are parallel.