1.
Tell which line through the given points is steeper. Show how you got the answer.Line 1: (-2,3)(3,5)Line 2: (3,1)(6,5)
Correct Answer
B. Line 2
Explanation
To determine which line is steeper, we can calculate the slope of each line. The slope of a line can be found by using the formula (y2 - y1) / (x2 - x1). For Line 1, the slope is (5 - 3) / (3 - (-2)) = 2 / 5. For Line 2, the slope is (5 - 1) / (6 - 3) = 4 / 3. Since 4/3 is greater than 2/5, Line 2 is steeper than Line 1.
2.
Tell whether the lines through the given points are parallel,perpendicular or neither.Line 1: (1,0)(7,4)Line 2: (7,0)(3,6)
Correct Answer
B. Perpendicular
Explanation
The lines through the given points are perpendicular because their slopes are negative reciprocals of each other. The slope of Line 1 is (4-0)/(7-1) = 4/6 = 2/3, and the slope of Line 2 is (6-0)/(3-7) = 6/-4 = -3/2. Since the slopes are negative reciprocals, the lines are perpendicular.
3.
Find the slope of the line that passes through the following points:(3,5 ) (5,6)
Correct Answer
B. 1/2
Explanation
To find the slope of a line passing through two points, we use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (3,5) and (5,6). Plugging these values into the formula, we get: slope = (6 - 5) / (5 - 3) = 1/2. Therefore, the slope of the line passing through these two points is 1/2.
4.
Line A passes through points (-8,3) and (-6,7)
Line B passes through points (-5,4) and (-3,3)
Are lines A and B parallel,perpendicular,or neither?
Correct Answer
B. Perpendicular
Explanation
The slopes of two lines can be used to determine if they are parallel, perpendicular, or neither. To find the slope of a line, we use the formula (y2 - y1) / (x2 - x1). For Line A, the slope is (7 - 3) / (-6 - (-8)) = 4 / 2 = 2. For Line B, the slope is (3 - 4) / (-3 - (-5)) = -1 / 2 = -0.5. Since the slopes of Line A and Line B are negative reciprocals of each other (2 and -0.5), the lines are perpendicular.
5.
Line A passes through points ( 0,9) and (6,5)
Line B passes through points (-6,-3) and (0,-7)
Are lines A and B parallel,perpendicular,or neither?
Correct Answer
A. Parallel
Explanation
The slopes of two lines can be used to determine if they are parallel, perpendicular, or neither. In this case, the slope of line A can be calculated as (5-9)/(6-0) = -4/6 = -2/3. Similarly, the slope of line B is (0-(-3))/(0-(-6)) = -3/6 = -1/2. Since the slopes of the two lines are different, they are not perpendicular. However, since the slopes are not equal but have a constant ratio of -2/3, the lines are parallel.
6.
Line A passes through points ( 5,1) and (-2,6)
Line B passes through points (-1,-1) and (5.5)
Are lines A and B parallel,perpendicular,or neither?
Correct Answer
C. Neither
Explanation
The given lines A and B are neither parallel nor perpendicular. In order for two lines to be parallel, their slopes must be equal. However, the slopes of lines A and B cannot be determined as the second point of line B is missing its y-coordinate. Similarly, for two lines to be perpendicular, the product of their slopes must be -1. Since the slopes cannot be determined, it cannot be determined if the lines are perpendicular. Thus, the correct answer is neither.
7.
Find the slope of the line passing through the points (2,1), (0,1).
Correct Answer
A. 0
Explanation
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula (y2-y1)/(x2-x1). In this case, the points are (2,1) and (0,1). Plugging the values into the formula, we get (1-1)/(0-2) = 0/(-2) = 0. Therefore, the slope of the line passing through these points is 0.
8.
Find the slope of the line passing through the points (2,5), (2,8).
Correct Answer
E. Undefined
Explanation
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1). In this case, the x-coordinates of both points are the same, which means the denominator of the formula becomes 0. Division by 0 is undefined in mathematics, so the slope of the line passing through these two points is undefined.
9.
What is the slope of the line passing through the points (4,2), (8,4)?
Correct Answer
D. 1/2
Explanation
The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the coordinates are (4,2) and (8,4). Plugging these values into the formula, we get (4 - 2) / (8 - 4) = 2 / 4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.
10.
Find the slope of the line passing through the points (-3,-3), (2,2).
Correct Answer
E. 1
Explanation
The slope of a line passing through two points can be found using the formula: slope = (change in y)/(change in x). In this case, the change in y is 2 - (-3) = 5, and the change in x is 2 - (-3) = 5. Therefore, the slope is 5/5 = 1.