Final answer:
The slopes of lines A and B are related by a factor of three; if line B's slope is 3, line A's slope is 1. This typically indicates increasing lines, but if line A is labeled as decreasing, there is a discrepancy. Figure A1's reference to slope in graphing reinforces the understanding of line equations.
Step-by-step explanation:
The question discusses the relationship between the slopes of two lines, where one line's slope is three times the slope of the other line. If we assume that the slope of line A is m, then the slope of line B would be 3m, since it's given that line B's slope is three times that of line A's slope. If line B prime (likely referring to a line parallel to line B) has a slope of 3, this tells us that line B also has a slope of 3 (since parallel lines have the same slope). Consequently, the slope of line A would be 3 divided by 3, which is 1. This implies that for every unit increase in the x-direction, line A rises by 1 unit in the y-direction. An increasing line would have a positive slope, while a decreasing line would have a negative slope. Therefore, if line A is described as a decreasing line and line B as an increasing one, there must be a typo because a slope of 1 indicates an increasing line.
Furthermore, the question states that a prime B prime passes through point A. Without additional information about point A or the equation of a prime B prime, we cannot ascertain more details. However, Figure A1 mentioned discusses the concepts of slope and the algebra of straight lines, which can help understand how the slope (m) and y-intercept (b) components define the line's equation and its graphical representation.