Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)%0D%0AResponses%0D%0A%0D%0ANo…these lines are parallel%0D%0ANo…these lines are parallel%0D%0A%0D%0ANo…these lines are perpendicular%0D%0ANo…these lines are perpendicular%0D%0A%0D%0AYou cannot tell without a graph%0D%0AYou cannot tell without a graph%0D%0A%0D%0AYes…these lines are not parallel%0D%0AYes…these lines are not parallel%0D%0A%0D%0AYes…these lines are perpendicular%0D%0AYes…these lines are perpendicular%0D%0A%0D%0AYes…these lines are parallel
No...these lines are not parallel
To determine if the lines intersect, we need to calculate the slopes of both lines.
Slope of the line passing through (3, 7) and (-2, -5):
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
Slope of the line passing through (4, 8) and (10, -2):
m2 = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
Since the slopes are not equal, the lines are not parallel.
Therefore, the line passing through (3, 7) and (-2, -5) intersects with the line passing through (4, 8) and (10, -2).
To determine if the lines intersect or not, we need to calculate the slopes of the two lines and compare them. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of the first line passing through (3, 7) and (-2, -5):
slope1 = (-5 - 7) / (-2 - 3)
slope1 = (-12) / (-5)
slope1 = 12/5
Now, let's calculate the slope of the second line passing through (4, 8) and (10, -2):
slope2 = (-2 - 8) / (10 - 4)
slope2 = (-10) / 6
slope2 = -5/3
Since the slopes of the two lines (12/5 and -5/3) are not equal, the lines are not parallel.
Therefore, the answer is: Yes, these lines are not parallel