Final answer:
The correct slopes for the line with a simplified ratio of 1/5 are A) 1/5 and C) -1/5, representing a positive and a negative slope respectively.
Step-by-step explanation:
The simplified ratio of the vertical side length to the horizontal side length of each triangle formed by the slope of a line is given as 1/5. This ratio can also be viewed as the slope of the line when considering a straight line on a graph. Given the options A) 1/5, B) 5/1, C) -1/5, D) -5/1, and E) 2/3, the correct slopes that can be represented by this ratio are A) 1/5, which is a positive slope, indicating a line rising from left to right, and C) -1/5, which is a negative slope, representing a line that falls from left to right.
Both positive and negative slopes can have the same absolute value but different directions. Option B) 5/1 has a much steeper ratio, while D) -5/1 also has a steeper ratio but in the negative direction, and E) 2/3 is not equivalent to the original ratio of 1/5 provided.