Let's break down the information given and fill in the blanks step-by-step.
First, we need to identify the role of the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in the equation [tex]\( y = 2 - 4x \)[/tex].
1. The [tex]\(x\)[/tex]-values are:
- In the context of a function, [tex]\(x\)[/tex] is the input variable. These are the values you choose independently to substitute into the equation [tex]\( y = 2 - 4x \)[/tex].
- Therefore, the [tex]\(x\)[/tex]-values are the independent variables.
2. The [tex]\(y\)[/tex]-values are:
- The value of [tex]\( y \)[/tex] depends on what value [tex]\( x \)[/tex] is. It is calculated based on the equation, taking into consideration the chosen [tex]\(x\)[/tex]-value.
- Hence, the [tex]\(y\)[/tex]-values are the dependent variables.
3. Finding the missing value for [tex]\( x = -1 \)[/tex]:
- To find the missing value, substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 2 - 4x \)[/tex].
- Perform the calculation:
[tex]\[
y = 2 - 4(-1)
\][/tex]
[tex]\[
y = 2 + 4
\][/tex]
[tex]\[
y = 6
\][/tex]
Putting it all together:
- The [tex]\(x\)[/tex]-values are the independent variables.
- The [tex]\(y\)[/tex]-values are the dependent variables.
- The missing value in the table for [tex]\( x = -1 \)[/tex] is [tex]\( y = 6 \)[/tex].
So, the completed statements are:
- The [tex]\(x\)[/tex]-values are the independent variables.
- The [tex]\(y\)[/tex]-values are the dependent variables.
- The missing value in the table for [tex]\(x = -1\)[/tex] is [tex]\( y = 6 \)[/tex].
