Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)ResponsesYes…these lines are not parallelYes…these lines are not parallelNo…these lines are parallelNo…these lines are parallelYes…these lines are parallelYes…these lines are parallelYes…these lines are perpendicularYes…these lines are perpendicularNo…these lines are perpendicularNo…these lines are perpendicularYou cannot tell without a graph
No…these lines are parallel
To determine if the lines intersect or are parallel, we can calculate the slopes of the two lines. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
For the first line passing through (3, 7) and (-2, -5):
m1 = (-5 - 7) / (-2 - 3) = (-12) / (-5) = 12/5 = 2.4
For the second line passing through (4, 8) and (10, -2):
m2 = (-2 - 8) / (10 - 4) = (-10) / 6 = -5/3 ≈ -1.6667
Since the slopes m1 and m2 are not equal, the lines are not parallel. Therefore, the correct response is:
Yes…these lines are not parallel
To determine if the lines intersect or are parallel, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
For the first line through points (3, 7) and (-2, -5), we can find the slope (m1) as follows:
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
The equation for this line can be written as:
y = (12/5)x + b1
Now let's calculate the slope (m2) for the second line through points (4, 8) and (10, -2):
m2 = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
The equation for this line can be written as:
y = (-5/3)x + b2
If the slopes of the two lines are equal, they are parallel. Otherwise, they are not parallel. Now we can compare the slopes:
m1 = 12/5
m2 = -5/3
Since the slopes are not equal, the lines are not parallel. Therefore, the correct response is:
Yes...these lines are not parallel