Final answer:
The correct explanation for why the slope of AB is equal to the slope of BC is because the points A, B, and C are collinear, meaning they lie on the same straight line, which maintains a constant slope between any two points.
Step-by-step explanation:
To determine which sentence explains why the slope of AB is equal to the slope of BC, one must understand the concept of slope in geometry. Slope is defined as the ratio of the rise (the change in y) over the run (the change in x) between two points on a line. If the points A, B, and C are collinear, it means that they lie on the same straight line, and therefore the slope between any two points on this line is the same.
Given this information, the correct answer is c) The points A, B, and C are collinear. If A, B, and C are points on the same straight line, the slope of AB will be equal to the slope of BC because the slope is consistent along a straight line. This can be confirmed by examining Figure A1 about Slope and the Algebra of Straight Lines that describes the slope as constant along a straight line.