Let's analyze and complete the statements step-by-step based on the given equation [tex]\( y = 2 - 4x \)[/tex] and the table.
1. The [tex]$x$[/tex]-values are listed in the left column of the table:
- -2
- -1
- 0
- 1
Therefore, the [tex]$x$[/tex]-values are the first values of each row (column).
2. The [tex]$y$[/tex]-values are listed in the right column of the table:
- 10 (for [tex]\( x = -2 \)[/tex])
- ? (for [tex]\( x = -1 \)[/tex])
- -2 (for [tex]\( x = 0 \)[/tex])
- -6 (for [tex]\( x = 1 \)[/tex])
Therefore, the [tex]$y$[/tex]-values are the second values of each row (column).
3. Now, we need to find the missing [tex]$y$[/tex]-value for [tex]\( x = -1 \)[/tex]. According to the equation [tex]\( y = 2 - 4x \)[/tex]:
- For [tex]\( x = -1 \)[/tex], substitute -1 into the equation for [tex]\( x \)[/tex]:
[tex]\[
y = 2 - 4(-1)
\][/tex]
- Simplify the equation:
[tex]\[
y = 2 + 4 = 6
\][/tex]
Therefore, the missing value in the table for [tex]\( x = -1 \)[/tex] is [tex]\( y = 6 \)[/tex].
Thus, we can complete the statements as follows:
- The [tex]$x$[/tex]-values are the first values of each row (column).
- The [tex]$y$[/tex]-values are the second values of each row (column).
- The missing value in the table for [tex]\( x = -1 \)[/tex] is [tex]\( y = 6 \)[/tex].
