Answer :
Sure! Let's create a table for the line [tex]\( y = 1 - 3x \)[/tex] where [tex]\( x \)[/tex] ranges from -2 to 2. We'll calculate the corresponding [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex].
### Step-by-Step Solution:
1. Identify the range of [tex]\( x \)[/tex] values:
- The [tex]\( x \)[/tex] values run from -2 to 2.
- So we have [tex]\( x = -2, -1, 0, 1, 2 \)[/tex].
2. Calculate the [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex] using the equation [tex]\( y = 1 - 3x \)[/tex]:
- For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 1 - 3(-2) = 1 + 6 = 7 \][/tex]
- For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 1 - 3(-1) = 1 + 3 = 4 \][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 1 - 3(0) = 1 \][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 1 - 3(1) = 1 - 3 = -2 \][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 1 - 3(2) = 1 - 6 = -5 \][/tex]
3. Construct the table with the calculated values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & 7 \\ -1 & 4 \\ 0 & 1 \\ 1 & -2 \\ 2 & -5 \\ \hline \end{array} \][/tex]
### Detailed Table:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = 7 \)[/tex].
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 4 \)[/tex].
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 1 \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( y = -2 \)[/tex].
- When [tex]\( x = 2 \)[/tex], [tex]\( y = -5 \)[/tex].
Thus, the completed table showing the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & 7 \\ -1 & 4 \\ 0 & 1 \\ 1 & -2 \\ 2 & -5 \\ \hline \end{array} \][/tex]
These are the respective [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values for the given line equation [tex]\( y = 1 - 3x \)[/tex] within the specified range.
### Step-by-Step Solution:
1. Identify the range of [tex]\( x \)[/tex] values:
- The [tex]\( x \)[/tex] values run from -2 to 2.
- So we have [tex]\( x = -2, -1, 0, 1, 2 \)[/tex].
2. Calculate the [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex] using the equation [tex]\( y = 1 - 3x \)[/tex]:
- For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 1 - 3(-2) = 1 + 6 = 7 \][/tex]
- For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 1 - 3(-1) = 1 + 3 = 4 \][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 1 - 3(0) = 1 \][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 1 - 3(1) = 1 - 3 = -2 \][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 1 - 3(2) = 1 - 6 = -5 \][/tex]
3. Construct the table with the calculated values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & 7 \\ -1 & 4 \\ 0 & 1 \\ 1 & -2 \\ 2 & -5 \\ \hline \end{array} \][/tex]
### Detailed Table:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = 7 \)[/tex].
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 4 \)[/tex].
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 1 \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( y = -2 \)[/tex].
- When [tex]\( x = 2 \)[/tex], [tex]\( y = -5 \)[/tex].
Thus, the completed table showing the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & 7 \\ -1 & 4 \\ 0 & 1 \\ 1 & -2 \\ 2 & -5 \\ \hline \end{array} \][/tex]
These are the respective [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values for the given line equation [tex]\( y = 1 - 3x \)[/tex] within the specified range.
