Final answer:
The line with the least rate of change is the line passing through (1, 1) and (7, 1) as it is horizontal with a slope of 0, indicating no change in the y-coordinate as the x-coordinate increases.
Step-by-step explanation:
The question involves determining which line has the least rate of change, which is equivalent to finding the line with the smallest slope. The slope of a line is calculated by the difference in the y-coordinates divided by the difference in the x-coordinates (rise over run). To compare the rates of change for the given lines, we can calculate the slope for each line using the two points provided.
- For the line passing through (1, -5) and (-9, -9), slope = (-9 - (-5)) / (-9 - 1) = (-4) / (-10) = 0.4.
- For the line passing through (1, 1) and (7, 1), slope = (1 - 1) / (7 - 1) = 0 / 6 = 0. This line is horizontal and has a slope of 0.
- For the line passing through (0, 0) and (-2, -1), slope = (-1 - 0) / (-2 - 0) = -1 / -2 = 0.5.
- For the line passing through (1, 1) and (-3, -6), slope = (-6 - 1) / (-3 - 1) = -7 / -4 = 1.75.
From these calculations, we can see that the line with points (1, 1) and (7, 1) has the least rate of change, which is 0, and it is a horizontal line.