To determine which property justifies the given statement, let's go through the provided information step by step:
1. We are given that [tex]\( x = 4 \)[/tex].
2. We are also given the equation [tex]\( y = 3x - 11 \)[/tex].
3. To find the value of [tex]\( y \)[/tex], we need to substitute [tex]\( x \)[/tex] with its given value in the equation [tex]\( y = 3x - 11 \)[/tex].
By substituting [tex]\( x = 4 \)[/tex] into the equation [tex]\( y = 3x - 11 \)[/tex], we get:
[tex]\[
y = 3 \cdot 4 - 11
\][/tex]
This step of replacing [tex]\( x \)[/tex] with its value (which is 4) in the equation [tex]\( y = 3x - 11 \)[/tex] is justified by the Substitution Property of Equality. This property states that if two values are equal, one value can be substituted for the other in an equation.
Therefore, the property that justifies the statement "If [tex]\( x = 4 \)[/tex] and [tex]\( y = 3x - 11 \)[/tex], then [tex]\( y = 3 \cdot 4 - 11 \)[/tex]" is the Substitution Property of Equality.
