Final answer:
Lines A and B have different slopes, so they are not parallel; only lines with identical slopes and different y-intercepts are parallel. The slope mentioned in Figure A1 is an example of a slope that would characterize parallel lines if matched by another line with a different y-intercept.
Step-by-step explanation:
Understanding the Relationship Between Slopes and Parallel Lines
When discussing the characteristics of straight lines in a coordinate system, the slope is a fundamental concept. It indicates how steep a line is and is calculated as the rise over the run (change in y over the change in x). In the case of Line A with a slope of -4.7 and Line B with a slope of 12.0, we can immediately determine that these two lines are not parallel because their slopes are not equal. Parallel lines must have the same slope and different y-intercepts. Line A and Line B, having distinctly different slopes, will eventually intersect at some point in the plane.
An example of equations that represent parallel lines can be seen in Figure A1, where the slope given is 3. Any other line with a slope of 3 but a different y-intercept would be parallel to the line described in Figure A1. In contrast, lines that are perpendicular to each other would have slopes that are negative reciprocals of each other. For instance, if another line had a slope of -1/3, it would be perpendicular to the line with a slope of 3 in Figure A1.