Line A passes through the points (-8, 5) and (-5, 4). Line B passes through the points (0, 1) and (4, -1). Which of the following describes the relationship between line A an line B?
Lines A and B are parallel, because they have the same slope
Lines A and B are parallel, because they have opposite reciprocal
slopes.
Lines A and B are perpendicular, because they have opposite reciprocal
slopes.
Lines A and B intersect, because their slopes have no relationship.
so find the slopes for A and B. If they are m1 and m2, then you know that
m1 = m2 means A||B
m1 * m2 = -1 means A⊥B
So let 'er rip.
thank you!
To determine the relationship between line A and line B, we first need to find the slopes of both lines.
The slope of line A can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Given that (-8, 5) and (-5, 4) are points on line A, we can calculate its slope:
Slope of line A = (4 - 5) / (-5 - (-8)) = -1 / 3
Similarly, we can find the slope of line B using the coordinates of (0, 1) and (4, -1):
Slope of line B = (-1 - 1) / (4 - 0) = -2 / 4 = -1 / 2
Now, comparing the slopes of line A and line B:
Slope of line A: -1/3
Slope of line B: -1/2
Since the slopes are different and not opposite reciprocals, lines A and B are not parallel or perpendicular.
Therefore, the correct answer is: Lines A and B intersect because their slopes have no relationship.
To determine the relationship between two lines, we need to examine their slopes.
For Line A passing through the points (-8, 5) and (-5, 4), we can use the formula for the slope of a line:
slope of Line A = (y2 - y1) / (x2 - x1)
Using the given points, we can substitute the values:
slope of Line A = (4 - 5) / (-5 - (-8))
Simplifying further:
slope of Line A = -1 / 3
Similarly, for Line B passing through the points (0, 1) and (4, -1), we can calculate its slope:
slope of Line B = (-1 - 1) / (4 - 0)
Simplifying further:
slope of Line B = -2 / 4
slope of Line B = -1 / 2
Now, let's compare the slopes:
The slope of Line A is -1/3, and the slope of Line B is -1/2.
Looking at the answer choices:
- "Lines A and B are parallel, because they have the same slope" is not correct because the slopes are different.
- "Lines A and B are parallel, because they have opposite reciprocal slopes" is also not correct as they do not have opposite reciprocal slopes.
- "Lines A and B are perpendicular, because they have opposite reciprocal slopes" is not correct either since the slopes are not opposite reciprocals.
Therefore, the correct answer is "Lines A and B intersect, because their slopes have no relationship."