Final answer:
Two parallel lines have equal slopes and different y-intercepts. Line A with a slope of -4.7 and Line B with a slope of 12.0 are not parallel due to their different slopes. Parallel lines maintain a constant distance by having the same rate of change and do not intersect. The correct answer is option A. parallel lines have the same slope.
Step-by-step explanation:
When analyzing the properties of parallel lines, it is important to understand the relationship between their slopes and their intercepts. Two parallel lines have the same slope because they maintain a constant distance from each other and never intersect. This is a fundamental concept in algebra that reflects the consistent rate of change along each line. According to the given figures, if Line A has a slope of -4.7 and Line B has a slope of 12.0, we can conclude that these lines are not parallel because their slopes are different. The unique slopes indicate varying angles in relation to the horizontal axis.
Moreover, parallel lines must have different y-intercepts, which is the point where a line crosses the y-axis. If two lines had the same y-intercept and the same slope, they would in fact be the same line. The difference in y-intercepts ensures that the lines, while never intersecting, also are not one and the same. Similarly, the x-intercepts, points where lines cross the x-axis, would be different for parallel lines due to their distinct y-intercepts and the consistency of their slopes. Therefore, parallel lines are characterized by equal slopes and unequal y-intercepts.