Sure, let's solve the equation [tex]\( y = 2x - 3 \)[/tex] by finding the corresponding [tex]\( y \)[/tex] values for specific [tex]\( x \)[/tex] values. We'll analyze a few [tex]\( x \)[/tex] values step by step.
Let's choose the following [tex]\( x \)[/tex] values: [tex]\( 0, 1, 2, 3, 4 \)[/tex].
1. For [tex]\( x = 0 \)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 2(0) - 3
\][/tex]
Simplifying this gives:
[tex]\[
y = -3
\][/tex]
2. For [tex]\( x = 1 \)[/tex]:
Substitute [tex]\( x = 1 \)[/tex] into the equation:
[tex]\[
y = 2(1) - 3
\][/tex]
Simplifying this gives:
[tex]\[
y = -1
\][/tex]
3. For [tex]\( x = 2 \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
y = 2(2) - 3
\][/tex]
Simplifying this gives:
[tex]\[
y = 1
\][/tex]
4. For [tex]\( x = 3 \)[/tex]:
Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
y = 2(3) - 3
\][/tex]
Simplifying this gives:
[tex]\[
y = 3
\][/tex]
5. For [tex]\( x = 4 \)[/tex]:
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = 2(4) - 3
\][/tex]
Simplifying this gives:
[tex]\[
y = 5
\][/tex]
Thus, the corresponding [tex]\( y \)[/tex] values for the [tex]\( x \)[/tex] values [tex]\( 0, 1, 2, 3, 4 \)[/tex] are:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
0 & -3 \\
1 & -1 \\
2 & 1 \\
3 & 3 \\
4 & 5 \\
\end{array}
\][/tex]
So, the list of [tex]\( y \)[/tex] values is: [tex]\([-3, -1, 1, 3, 5]\)[/tex].
