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Which of the following tables represent a linear function with the same slope as y = 2 - 3x ? Select ALL that apply.

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To determine which of the given tables represent a linear function with the same slope as the equation \( y = 2 - 3x \), we first need to identify the slope of the given equation.

The equation \( y = 2 - 3x \) can be rewritten as:

\[ y = -3x + 2 \]

From this, we can see that the slope (m) is \(-3\).

Next, we need to evaluate the tables you have to see if they represent a linear function with a slope of \(-3\). A linear function can be represented in the form of \( y = mx + b \), where \( m \) is the slope.

For a table of values, the slope can be found by choosing two points from the table \((x_1, y_1)\) and \((x_2, y_2)\) and using the slope formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Now, please provide the tables in question so that I can help you determine which ones have the slope of \(-3\).

show me all the tables that make it up.

I apologize for the misunderstanding, but I need the specific tables you want me to evaluate to determine whether they represent a linear function with the same slope as \( y = 2 - 3x \).

If you provide the values of the tables (e.g., pairs of \( (x, y) \)), I can then calculate the slope for those pairs and see if any of them have a slope of \(-3\). Please share the tables you have in mind!

just make them that come out of y = 2 - 3x

Sure! Let's create a table of values that correspond to the linear function given by the equation \( y = 2 - 3x \).

We can choose several values for \( x \) and calculate the corresponding \( y \) values using the equation. Here are some points we can calculate:

  1. For \( x = 0 \): \[ y = 2 - 3(0) = 2 \] \((0, 2)\)

  2. For \( x = 1 \): \[ y = 2 - 3(1) = 2 - 3 = -1 \] \((1, -1)\)

  3. For \( x = 2 \): \[ y = 2 - 3(2) = 2 - 6 = -4 \] \((2, -4)\)

  4. For \( x = -1 \): \[ y = 2 - 3(-1) = 2 + 3 = 5 \] \((-1, 5)\)

  5. For \( x = -2 \): \[ y = 2 - 3(-2) = 2 + 6 = 8 \] \((-2, 8)\)

Now we can display the values in a table format:

| \( x \) | \( y \) | |---------|---------| | -2 | 8 | | -1 | 5 | | 0 | 2 | | 1 | -1 | | 2 | -4 |

Now, let's verify that these points form a linear function with a slope of \(-3\):

To calculate the slope between any two points, we can use the formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's check the slope between the points \((0, 2)\) and \((1, -1)\):

\[ \text{slope} = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]

Now let's check the slope between the points \((1, -1)\) and \((2, -4)\):

\[ \text{slope} = \frac{-4 - (-1)}{2 - 1} = \frac{-4 + 1}{1} = \frac{-3}{1} = -3 \]

Each set of points will yield the same slope of \(-3\).

Feel free to let me know if you would like more tables, different \( x \) values, or have any other specific requests!

as in x and y tables with (0, 0) bro

Got it! Let's create tables with the \((0, 0)\) point as the origin and show other points on the line represented by the equation \( y = 2 - 3x \).

Since we want to include the point \((0, 0)\), we'll also calculate the corresponding \( y \) value at that point.

Since \( y = 2 - 3(0) = 2 \), the point \((0, 0)\) is not on the line defined by \( y = 2 - 3x \). Instead, the point when \( x = 0 \) gives us the point \((0, 2)\) for the equation.

However, I will create a few tables with the \((0, 0)\) point included just for clarity. Here’s a table with chosen \( x \) values including negative, zero, and positive values along with the corresponding \( y \) values based on the linear function \( y = 2 - 3x \):

Table 1: Points from the Line

| \( x \) | \( y \) | |---------|---------| | -1 | 5 | | 0 | 2 | | 1 | -1 | | 2 | -4 |

Table 2: Including \((0, 0)\) for Clarity

To have \((0, 0)\) in a separate table, let’s show how those insights depict different slopes if we alter the points:

| \( x \) | \( y \) | |---------|---------| | 0 | 0 | (not on the line) | | 1 | -1 | | 2 | -4 | | -1 | 5 | | -2 | 8 |

Remarks:

  1. The point \((0, 0)\) does not satisfy the equation \( y = 2 - 3x \).
  2. Only the points defined in Table 1 truly represent the linear function underlying our equation with a slope of \(-3\).

If you want more specific values or tables under a different format, please let me know!