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This quiz is designed to assess if you know how to find a slope given two points on a line. You will also be assessed on steepness of a given slope and horizontal and undefined slopes.
Questions and Answers
1.
Find the slope of the line passing through the points (2,1), (0,1).
A.
0
B.
1
C.
1/2
D.
2/1
E.
-1
Correct Answer
A. 0
Explanation The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the points are (2,1) and (0,1). Plugging these 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.
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2.
Find the slope of the line passing through the points (2,5), (2,8).
A.
1/2
B.
-3
C.
-1/2
D.
2
E.
Undefined
Correct Answer
E. Undefined
Explanation The slope of a line passing through two points is found using the formula (y2 - y1) / (x2 - x1). In this case, the x-coordinates of both points are the same (2), which means the denominator of the formula would be 0. Division by zero is undefined in mathematics, so the slope of the line passing through these points is also undefined.
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3.
The slope of the line passing through the points (1,4), (-7,4) is ___________.
Correct Answer horizontal, 0
Explanation The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, both points have the same y-coordinate of 4, indicating that there is no change in the y-coordinate. Therefore, the change in y-coordinates is 0. Since any number divided by 0 is undefined, the slope of the line passing through these points is undefined. In terms of slope types, a line with an undefined slope is considered to be vertical, not horizontal. Therefore, the given answer of "horizontal" is incorrect.
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4.
What is the slope of the line passing through the points (4,2), (8,4)?
A.
-1/2
B.
2
C.
8
D.
1/2
E.
-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.
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5.
Find the slope of the line passing through the points (-6,2), (0,-6).
A.
-6
B.
2
C.
-4/3
D.
0
E.
-3/1
Correct Answer
C. -4/3
Explanation The slope of a line passing through two points can be found using the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (-6,2) and (0,-6). Plugging these values into the formula, we get: slope = (-6 - 2) / (0 - (-6)) = -8 / 6 = -4/3. Therefore, the correct answer is -4/3.
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6.
Find the slope of the line passing through the points (-3,-3), (2,2).
A.
-3
B.
3
C.
2
D.
-2
E.
1
Correct Answer
E. 1
Explanation The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (-3,-3) and (2,2). Plugging these values into the formula, we get (2 - (-3)) / (2 - (-3)) = 5 / 5 = 1. Therefore, the slope of the line passing through these points is 1.
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7.
Find the slope of the line passing through the points (5,-1), (-2,-3).
A.
2/7
B.
-5/2
C.
-1
D.
-2/7
E.
-3
Correct Answer
A. 2/7
Explanation To find the slope of a line passing through two points, we use the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (5, -1) and (-2, -3). Plugging these values into the formula, we get (-3 - (-1)) / (-2 - 5) = -2 / -7 = 2/7. Therefore, the slope of the line passing through these points is 2/7.
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