To determine which property justifies the statement "if [tex]\( y = 7 \)[/tex], then [tex]\( 7 = y \)[/tex]", let's review the relevant properties of equality.
1. Reflexive Property: This states that any number is equal to itself, i.e., [tex]\( a = a \)[/tex]. This does not involve switching the sides of the equation.
2. Symmetric Property: This states that if [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]. This property specifically indicates that if one quantity equals another, we can reverse the sides of the equation.
3. Identity Property: This involves the concept that there is an element (usually 0 or 1 in addition and multiplication) that, when combined with another element, does not change the value of that element, i.e., [tex]\( a + 0 = a \)[/tex] or [tex]\( a \cdot 1 = a \)[/tex]. This is not relevant to the equality of two variables.
4. Transitive Property: This states that if [tex]\( a = b \)[/tex] and [tex]\( b = c \)[/tex], then [tex]\( a = c \)[/tex]. This property involves three quantities and their equal relationships, which is not directly applicable to our given statement since it only involves two quantities.
Given the statement "if [tex]\( y = 7 \)[/tex], then [tex]\( 7 = y \)[/tex]", we observe that the sides of the equation are reversed. The property that allows us to make this reversal is the Symmetric Property.
Therefore, the property that justifies the statement is:
C. Symmetric Property
