The problem asks to create a table of $x$ and $y$ values for the line $3x + 2y = 6$, where $x$ ranges from $-1$ to $3$.

1. Problem Description

The problem asks to create a table of $x$ and $y$ values for the line $3x + 2y = 6$, where $x$ ranges from $-1$ to $3$.

2. Solution Steps

We are given the equation $3x + 2y = 6$. We need to solve for $y$ in terms of $x$.

$2y = 6 - 3x$

$y = \frac{6 - 3x}{2}$

Now, we can create a table of $x$ and $y$ values for $x$ from $-1$ to $3$.

$x = -1$:

$y = \frac{6 - 3(-1)}{2} = \frac{6 + 3}{2} = \frac{9}{2} = 4.5$

$x = 0$:

$y = \frac{6 - 3(0)}{2} = \frac{6}{2} = 3$

$x = 1$:

$y = \frac{6 - 3(1)}{2} = \frac{6 - 3}{2} = \frac{3}{2} = 1.5$

$x = 2$:

$y = \frac{6 - 3(2)}{2} = \frac{6 - 6}{2} = \frac{0}{2} = 0$

$x = 3$:

$y = \frac{6 - 3(3)}{2} = \frac{6 - 9}{2} = \frac{-3}{2} = -1.5$

The table of $x$ and $y$ values is:

| x | y |

|----|-----|

| -1 | 4.5 |

| 0 | 3 |

| 1 | 1.5 |

| 2 | 0 |

| 3 | -1.5|

3. Final Answer

The table of x and y values is:

| x | y |

|----|-----|

| -1 | 4.5 |

| 0 | 3 |

| 1 | 1.5 |

| 2 | 0 |

| 3 | -1.5|