Final answer:
The slope of a line between two points is determined by the difference in the y-values over the difference in the x-values. For the points (2,2) and (-2,1), the slope is 1/4, and for (-2,4) and (0,-1), the slope is -5/2. Another provided example gives a slope of approximately 4.5 for the points (1, 0.1) and (7, 26.8).
Step-by-step explanation:
Calculating the Slope of a Line
The slope of a line measures the steepness of the line and is calculated by finding the change in vertical distance (rise) over the change in horizontal distance (run) between two points on a line. To calculate the slope, you use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
The slope for a line passing through the points (2,2) and (-2,1) is calculated as follows:
(1 - 2) / (-2 - 2) = -1 / -4 which simplifies to 1/4. Therefore, Option A. 1/4 is correct.
The slope for a line passing through the points (-2,4) and (0,-1) is calculated as follows:
(-1 - 4) / (0 + 2) = -5 / 2, which simplifies to -5/2. Hence, Option B. -5/2 is correct.
Finally, for the points given in the reference, Point 1: (1, 0.1) and Point 2: (7, 26.8), the slope is (26.8 - 0.1) / (7 - 1) = 26.7 / 6, which equals 4.45, so the closest answer would be b. 4.5.