Part A: To identify which two numbers represented by the dots on the number line are opposites, we need to look for pairs that are equidistant from zero (0) but on opposite sides of it.
Looking at the number line with the given dots: -15, -5, 10, 15, 20, 25, and 35, we can find the opposites by finding pairs with the same absolute distance from zero but one is negative and the other positive.
The numbers that are opposites are: -15 and 15.
Part B: The relationship of the opposites to zero (0) is what makes them opposites. Zero is the midpoint on the number line, and any number equidistant from zero but on the opposite sides is considered an opposite pair.
In this case, -15 and 15 are opposites because they are both 15 units away from zero, but one is to the left (negative side) and the other to the right (positive side) of zero. When we add a negative number to its positive counterpart, or vice versa, the result is always zero. For example, -15 + 15 = 0.
This relationship is true because the negative sign indicates a lower value and the positive sign indicates a higher value. Thus, -15 and 15 are opposites because they have the same absolute value but are on opposite sides of zero on the number line.