To determine which entry in the table does not correctly fit the given relationship [tex]\( y = -2x + 3 \)[/tex], we need to check each pair of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values and see if they satisfy the equation.
Let's check each entry:
1. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -2(1) + 3 = -2 + 3 = 1
\][/tex]
However, the table lists [tex]\( y = 2 \)[/tex] for [tex]\( x = 1 \)[/tex]. This does not match the calculated [tex]\( y \)[/tex]. Therefore, the entry for [tex]\( x = 1 \)[/tex] is incorrect.
Let's confirm the rest to ensure they are consistent with the function.
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -2(2) + 3 = -4 + 3 = -1
\][/tex]
The table lists [tex]\( y = -1 \)[/tex] for [tex]\( x = 2 \)[/tex]. This is correct.
3. For [tex]\( x = 3 \)[/tex]:
[tex]\[
y = -2(3) + 3 = -6 + 3 = -3
\][/tex]
The table lists [tex]\( y = -3 \)[/tex] for [tex]\( x = 3 \. This is correct.
4. For \( x = 4 \)[/tex]:
[tex]\[
y = -2(4) + 3 = -8 + 3 = -5
\][/tex]
The table lists [tex]\( y = -5 \)[/tex] for [tex]\( x = 4 \. This is correct.
Therefore, the incorrect entry in the table corresponds to \( x = 1 \)[/tex].
So, the correct answer is:
[tex]\[
\x = 1
\][/tex]
