Doradiazperez02idn
Answered

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3) \begin{tabular}{rl|}
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
2 & 8.5 \\
1 & 4.5 \\
0 & 0.5 \\
-1 & -3.5 \\
-2 & -7.5 \\
\end{tabular}

Given the equation [tex]$y = 4x + 0.5$[/tex], complete the table for the corresponding [tex]$y$[/tex] values for each [tex]$x$[/tex].

Sagot :

GinnyAnsweridn
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].
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