Answer:
7. the slope of the line containing the points (3, 4) and (2, 6) is -2.
8. the slope of the line containing the points (-2, -1) and (2, -3) is -1/2.
Explanation:
7. To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line through those two points using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (3, 4) and (x2, y2) = (2, 6). Substituting these values into the formula, we get:
m = (6 - 4) / (2 - 3) = -2
So the slope of the line containing the points (3, 4) and (2, 6) is -2. Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2. Therefore, the answer is m = -2.
8. To find the slope of a line that is perpendicular to the line containing the points (-2, -1) and (2, -3), we first need to find the slope of the line through those two points using the same formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-2, -1) and (x2, y2) = (2, -3). Substituting these values into the formula, we get:
m = (-3 - (-1)) / (2 - (-2)) = -2 / 4 = -1/2
So the slope of the line containing the points (-2, -1) and (2, -3) is -1/2. To find the slope of a line that is perpendicular to this line, we need to take the negative reciprocal of -1/2, which is 2/1 or simply 2. Therefore, the answer is m = 2.