Final answer:
The equation −7k=−42 is solved using the Division Property of Equality when dividing both sides by -7 to find that k=6.
Step-by-step explanation:
The property of equality demonstrated when solving the equation −7k=−42 and finding that k=6 is the Division Property of Equality. When we divide both sides of the equation by -7, we maintain the balance of the equation. The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal. This property is in line with the rule that when a number is divided by another number, it follows multiplication rules for the sign. Therefore, dividing −42 by −7 results in +6 because a negative divided by a negative is a positive.