To solve for [tex]\( y \)[/tex] in the given equation [tex]\( 2x - 3 = 4y \)[/tex] for different values of [tex]\( x \)[/tex], we will rearrange the equation and then substitute each [tex]\( x \)[/tex] value to find the corresponding [tex]\( y \)[/tex] values. Let's go through it step by step:
1. Rearrange the equation:
Given equation:
[tex]\[
2x - 3 = 4y
\][/tex]
To solve for [tex]\( y \)[/tex], isolate [tex]\( y \)[/tex] on one side:
[tex]\[
4y = 2x - 3
\][/tex]
[tex]\[
y = \frac{2x - 3}{4}
\][/tex]
2. Substitute the given [tex]\( x \)[/tex] values and solve for [tex]\( y \)[/tex]:
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = \frac{2(-1) - 3}{4} = \frac{-2 - 3}{4} = \frac{-5}{4} = -1.25
\][/tex]
- For [tex]\( x = -6 \)[/tex]:
[tex]\[
y = \frac{2(-6) - 3}{4} = \frac{-12 - 3}{4} = \frac{-15}{4} = -3.75
\][/tex]
- For [tex]\( x = -4 \)[/tex]:
[tex]\[
y = \frac{2(-4) - 3}{4} = \frac{-8 - 3}{4} = \frac{-11}{4} = -2.75
\][/tex]
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = \frac{2(-2) - 3}{4} = \frac{-4 - 3}{4} = \frac{-7}{4} = -1.75
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = \frac{2(0) - 3}{4} = \frac{0 - 3}{4} = \frac{-3}{4} = -0.75
\][/tex]
3. Summarize the results in the table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
x & -1 & -6 & -4 & -2 & 0 \\
\hline
y & -1.25 & -3.75 & -2.75 & -1.75 & -0.75 \\
\hline
\end{tabular}
\][/tex]
These are the [tex]\( y \)[/tex] values corresponding to the given [tex]\( x \)[/tex] values for the equation [tex]\( 2x - 3 = 4y \)[/tex].
