Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses
Yes…these lines are parallel
Yes…these lines are parallel
Yes…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are not parallel
Yes…these lines are not parallel
No…these lines are parallel
No…these lines are parallel
You cannot tell without a graph
You cannot tell without a graph
No…these lines are perpendicular
You cannot tell without a graph
To determine if the lines intersect, we need to find the slopes of both lines.
The slope of the line passing through (3,7) and (-2,-5) is given by:
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
The slope of the line passing through (4,8) and (10,-2) is given by:
m2 = (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 correct answer is:
Yes…these lines are not parallel
To determine if the lines intersect or not, we can use the slope-intercept form of a line, which is y = mx + b. The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
For the first line passing through (3, 7) and (-2, -5), we can calculate the slope as follows:
m1 = (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5
For the second line passing through (4, 8) and (10, -2), we can calculate the slope as follows:
m2 = (-2 - 8) / (10 - 4)
= -10 / 6
= -5/3
Since the slopes of the two lines, m1 and m2, are not equal, the lines are not parallel. Thus, the correct answer is: "Yes…these lines are not parallel."