Does the line through (3%2C 7) and (-2%2C -5) intersect with the line through (4%2C 8) and (10%2C -2)%3F(1 point) Responses Yes…these lines are not parallel Yes…these lines are not parallel No…these lines are perpendicular No…these lines are perpendicular Yes…these lines are parallel Yes…these lines are parallel Yes…these lines are perpendicular Yes…these lines are perpendicular No…these lines are parallel No…these lines are parallel You cannot tell without a graph
Yes…these lines are not parallel
To determine whether the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we can use the slope-intercept form of a straight line equation and compare the slopes of the two lines.
1. Find the slope of the first line:
slope = (y2 - y1) / (x2 - x1)
slope = (-5 - 7) / (-2 - 3)
slope = (-12) / (-5)
slope = 12/5
2. Find the slope of the second line:
slope = (y2 - y1) / (x2 - x1)
slope = (-2 - 8) / (10 - 4)
slope = (-10) / (6)
slope = -5/3
Now, we can compare the slopes to determine the relationship between the lines:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals of each other (i.e., multiplying one slope by -1 gives the other slope), the lines are perpendicular.
- If the slopes are neither equal nor negative reciprocals of each other, the lines will intersect.
3. Compare the slopes:
12/5 is not equal to -5/3, and they are not negative reciprocals of each other.
Since the slopes are neither equal nor negative reciprocals, we can conclude that the lines are not parallel or perpendicular. Therefore, the answer is "No…these lines are not parallel" and "No…these lines are not perpendicular."
To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we need to check if the slopes of the two lines are equal and if they are not parallel.
1. Find the slope of the first line:
The formula for slope (m) is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (3, 7) and (-2, -5):
m1 = (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
2. Find the slope of the second line:
Using the coordinates (4, 8) and (10, -2):
m2 = (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
3. Check if the slopes are equal:
Since m1 = 12/5 and m2 = -5/3 are not equal, the lines are not parallel.
Therefore, the correct response is: Yes, these lines are not parallel.