Sure, let's solve the problem step-by-step.
You are given the equation [tex]\( y = 4x + 0.5 \)[/tex] and a table with values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. We want to find the missing [tex]\( x \)[/tex] value when [tex]\( y = 9 \)[/tex].
Here's the given table again for reference:
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|:------:|:--------:|
| 2 | 13 |
| | 9 |
| 0 | 5 |
| -1 | -1 |
| -2 | -13 |
Step 1: Identify the known values
1. When [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 4(2) + 0.5 = 8 + 0.5 = 13
\][/tex]
2. When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 4(0) + 0.5 = 0 + 0.5 = 5
\][/tex]
3. When [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 4(-1) + 0.5 = -4 + 0.5 = -1
\][/tex]
4. When [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 4(-2) + 0.5 = -8 + 0.5 = -13
\][/tex]
Step 2: Find the missing [tex]\( x \)[/tex] when [tex]\( y = 9 \)[/tex]
The equation [tex]\( y = 4x + 0.5 \)[/tex] can be rearranged to solve for [tex]\( x \)[/tex]:
[tex]\[
9 = 4x + 0.5
\][/tex]
Subtract 0.5 from both sides:
[tex]\[
9 - 0.5 = 4x
\][/tex]
[tex]\[
8.5 = 4x
\][/tex]
Divide both sides by 4 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{8.5}{4}
\][/tex]
[tex]\[
x = 2.125
\][/tex]
Step 3: Compile all the values
Now that we have found the missing [tex]\( x \)[/tex] value, we can complete the table:
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|:------: |:--------:|
| 2 | 13 |
| 2.125 | 9 |
| 0 | 5 |
| -1 | -1 |
| -2 | -13 |
So, the complete set of [tex]\( x \)[/tex] values is [tex]\( [2, 2.125, 0, -1, -2] \)[/tex].
