Final answer:
The slope of the line through the points (6,6) and (8,8) is calculated using the slope formula and is found to be 1, indicating direct variation and a consistent rise over run ratio along the line.
Step-by-step explanation:
To find the slope of the line through the given points (6,6) and (8,8), you can use the slope formula, which is (change in y) / (change in x), also known as Δy/Δx or (y2 - y1) / (x2 - x1). In this case, you would calculate the slope as follows:
- First point (x1, y1) = (6, 6)
- Second point (x2, y2) = (8, 8)
- Change in y (Δy) = y2 - y1 = 8 - 6 = 2
- Change in x (Δx) = x2 - x1 = 8 - 6 = 2
- Slope (m) = Δy / Δx = 2 / 2 = 1
Thus, the slope of the line is 1. This indicates direct variation, meaning that for every increase of 1 on the horizontal axis (x), there is an equal rise of 1 on the vertical axis (y), which is consistent with the definition of slope given for a straight line in the reference