Final answer:
The slope of line e is the same as the slope of line d because parallel lines have identical slopes. The slope of line d, passing through points (2,2) and (5,7), is 5/3. Consequently, the slope of line e is also 5/3.
Step-by-step explanation:
The student asked about the slope of line e which is parallel to line d. The slope of a line in a two-dimensional plane represents how steep the line is, and it's calculated by the rise over the run (change in y over change in x). To calculate the slope of line d, we use the coordinates of the two given points (2, 2) and (5, 7).
Using the formula for slope (m) which is (y2 - y1) / (x2 - x1), we get:
Slope of line d = (7 - 2) / (5 - 2) = 5 / 3.
Since lines that are parallel have the same slope, line e, which is parallel to line d, would also have a slope of 5 / 3. Therefore, the slope of line e is indeed 5/3 or 1.667.