1.
Find the slope of the line containing points (5, 3) and (2, 1)
Correct Answer
A. 2/3
Explanation
To find the slope of a line, we use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (5, 3) and (2, 1). Plugging these values into the formula, we get (1 - 3) / (2 - 5), which simplifies to -2 / -3. Simplifying further, we get 2/3. Therefore, the slope of the line is 2/3.
2.
Find the slope of the line containing points (4, 1) and (1, 0).
Correct Answer
C. 3
Explanation
The slope of a line 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. In this case, the coordinates are (4, 1) and (1, 0). Plugging these values into the formula, we get (0 - 1) / (1 - 4) = -1 / -3 = 1/3. However, the given answer is 3, which is incorrect.
3.
Find the slope of the line containing points (5, 2) and (3, 4)
Correct Answer
B. -1
Explanation
The slope of a line 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. Plugging in the given coordinates, we get (4 - 2) / (3 - 5) = -2 / -2 = 1. Therefore, the slope of the line containing the points (5, 2) and (3, 4) is 1.
4.
Find the slope of the line containing points (8, 5) and (6, 1).
Correct Answer
B. 2
Explanation
The slope of a line 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. In this case, the coordinates are (8, 5) and (6, 1). Plugging these values into the formula, we get (1 - 5) / (6 - 8) = -4 / -2 = 2. Therefore, the slope of the line is 2.
5.
Find the slope of the line containing points (6, 8) and (2, 10)
Correct Answer
D. -1/2
Explanation
The slope of a line 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. In this case, the coordinates are (6, 8) and (2, 10). Plugging these values into the formula, we get (10 - 8) / (2 - 6) = 2 / -4 = -1/2. Therefore, the slope of the line is -1/2.
6.
Find the slope of the line containing points (4, 5) and (1, 5)
Correct Answer
A. 0
Explanation
The slope of a line is calculated by finding the difference in the y-coordinates and dividing it by the difference in the x-coordinates of two points on the line. In this case, the y-coordinates of both points are the same (5), so the difference in the y-coordinates is 0. The x-coordinates of the two points are 4 and 1, so the difference in the x-coordinates is 3. Dividing 0 by 3 gives a slope of 0.
7.
Find the slope of the line containing points (4, 5) and (4, 1).
Correct Answer
B. Undefined
Explanation
The slope of a line is calculated using the formula (change in y)/(change in x). In this case, the x-coordinate of both points is the same (4), which means there is no change in x. When there is no change in x, the denominator becomes zero, resulting in an undefined value for the slope. Therefore, the correct answer is undefined.