Final answer:
The line with the greatest slope is the one passing through points (2,6) and (4,4), with a slope of -1. Points C (2,6) and D (4,4) answer the question correctly.
Step-by-step explanation:
To determine which of the points (1,0), (8,4), (2,6), (4,4) is on the line with the greatest slope, we need to calculate the slopes of the lines passing through these points. Since slope is the ratio of the difference in the y-coordinates to the difference in the x-coordinates (rise over run), we can calculate the slope of the line through any two points A (x1, y1) and B (x2, y2) using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
For point A (1,0) and point B (8,4):
slope = (4 - 0) / (8 - 1) = 4 / 7 \(\approx 0.57)
For point A (2,6) and point B (4,4):
slope = (4 - 6) / (4 - 2) = -2 / 2 = -1
The slope for the line through (2,6) and (4,4) is -1, which is greater in absolute value than the slope of the line through (1,0) and (8,4). Therefore, the points (2,6) and (4,4) are on the line with the greatest slope. Points C (2,6) and D (4,4) are correct. Points (1,0) and (8,4) have a less steep line compared to the line through points (2,6) and (4,4).