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

Question

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

Answer 1

We can determine if two lines intersect by checking if their slopes are different. If the slopes are different, the lines intersect.

First, let's find the slope of the line passing through (3, 7) and (-2, -5):

slope = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5

Now, let's find the slope of the line passing through (4, 8) and (10, -2):

slope = (y2 - y1) / (x2 - x1)
= (-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. Therefore, they will intersect.

So, the correct response is: Yes… these lines are not parallel.

Answer 2

To determine whether the lines intersect or not, we can calculate the slopes of both lines and compare them.

1. Calculate the slope of the first line:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-5 - 7) / (-2 - 3)
Slope = -12 / -5
Slope = 12/5

2. Calculate the slope of the second line:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-2 - 8) / (10 - 4)
Slope = -10 / 6
Slope = -5/3

Since the slopes of the two lines, 12/5 and -5/3, are not equal, the lines are not parallel.

To determine if the lines are perpendicular, we can check if the product of their slopes is equal to -1 (since the slopes of perpendicular lines are negative reciprocals of each other).

Calculate the product of the slopes:
(12/5) * (-5/3) = (-60/15) = -4

Since the product is not equal to -1, the lines are not perpendicular.

Therefore, the correct answer is:
No…these lines are not parallel
No…these lines are not perpendicular

Answer 3

To determine whether the lines intersect, we can calculate the slopes of the two lines.

Let's first find the slope of the line through (3, 7) and (-2, -5):

Slope = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5

Now, let's find the slope of the line through (4, 8) and (10, -2):

Slope = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3

Since the slopes of the two lines are not equal, the lines are not parallel.

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