Final answer:
The slopes of two parallel lines are equal, which is shown in their straight-line equations of the form y = mx + b, where m represents the slope.
Step-by-step explanation:
If two lines are parallel, the relationship between their slopes is that the slopes are equal. According to the principles of the algebra of straight lines, the equation of a straight line is given by y = mx + b, where m represents the slope of the line and b is the y-intercept. For parallel lines, since they never intersect and are always the same distance apart, their slopes must be the same. Therefore, the correct answer to the student's question is that the slopes are equal.
Looking at Figure A1 as an example, if we have another line parallel to the one in the figure, it will also have a slope of 3 since the rise over run ratio remains consistent. The y-intercept, b, can be different, but the slope, m, must remain the same for the lines to maintain parallelism.
When referring to slopes, the term 'perpendicular' is used to describe slopes of lines that intersect to form a right angle, which would mean their slopes are negative reciprocals of each other, not the case with parallel lines.