## Answer :

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].