Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point) Responses You cannot tell without a graph You cannot tell without a graph Yes…these lines are not parallel Yes…these lines are not parallel Yes…these lines are perpendicular Yes…these lines are perpendicular Yes…these lines are parallel Yes…these lines are parallel No…these lines are parallel No…these lines are parallel No…these lines are perpendicular

Question

Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point) Responses You cannot tell without a graph You cannot tell without a graph Yes…these lines are not parallel Yes…these lines are not parallel Yes…these lines are perpendicular Yes…these lines are perpendicular Yes…these lines are parallel Yes…these lines are parallel No…these lines are parallel No…these lines are parallel No…these lines are perpendicular

Answer 1

You cannot tell without a graph

Answer 2

To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we need to find the slopes of these two lines.

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

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

For the first line passing through (3, 7) and (-2, -5):

m1 = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5

For the second line passing through (4, 8) and (10, -2):

m2 = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3

Since the slopes of the two lines are different (12/5 and -5/3), these lines are not parallel.

Hence, the correct answer is: Yes, these lines are not parallel.

Answer 3

To determine if the lines intersect or not, we can calculate the slopes of the two lines.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)

For the first line passing through (3, 7) and (-2, -5):
slope1 = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5

For the second line passing through (4, 8) and (10, -2):
slope2 = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3

If the slopes of the two lines are equal, then the lines are parallel. If the slopes are negative reciprocals (i.e., the product of slopes is -1), then the lines are perpendicular. Otherwise, the lines will intersect.

Let's calculate the product of the slopes:
slope1 * slope2 = (12/5) * (-5/3) = -12/3 = -4

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

Also, the slopes are not equal (12/5 != -5/3), so the lines are not parallel.

Therefore, the lines do intersect.