Question 49

The function table below is intended to represent the relationship [tex]\( y = -2x + 3 \)[/tex]. However, one of the entries for [tex]\( y \)[/tex] does not correctly fit the relationship with [tex]\( x \)[/tex].

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
1 & 2 \\
\hline
2 & -1 \\
\hline
3 & -3 \\
\hline
4 & -5 \\
\hline
\end{tabular}
\][/tex]

For which value of [tex]\( x \)[/tex] is the given [tex]\( y \)[/tex] incorrect in the table?

A. [tex]\( x = 3 \)[/tex]
B. [tex]\( x = 1 \)[/tex]
C. [tex]\( x = 4 \)[/tex]
D. [tex]\( x = 2 \)[/tex]



Answer :

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]