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 parallel
You cannot tell without a graph
Yes…these lines are not parallel
Yes…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are parallel
You cannot tell without a graph.
To determine if two lines intersect, we need to find their slopes. Let's calculate the slopes of the two lines:
Line 1: (3, 7) and (-2, -5)
Slope of Line 1 = (change in y) / (change in x) = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5
Line 2: (4, 8) and (10, -2)
Slope of Line 2 = (change in y) / (change in x) = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3
Since the slopes of the two lines, 12/5 and -5/3, 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, we can use the slope-intercept form of a line equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope of the line passing through (3, 7) and (-2, -5), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points, the slope of the first line is:
m1 = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5
Similarly, to find the slope of the line passing through (4, 8) and (10, -2), we apply the same formula:
m2 = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3
Now, we compare the slopes. If the slopes of two lines are equal, they are parallel. If the slopes are negative reciprocals of each other (meaning multiplying them would result in -1), the lines are perpendicular.
Comparing 12/5 and -5/3, we can see that they are not equal, so the lines are not parallel.
Also, the slopes 12/5 and -5/3 are not negative reciprocals of each other since (12/5) * (-5/3) ≠ -1. Therefore, the lines are not perpendicular.
Hence, the correct answer is "No…these lines are not parallel."