Question
Which of the following tables represent a linear function with the same slope as y = 2 - 3x ? Select ALL that apply.
Answers
Answer
show me all the tables that make it up.
Answer
just make them that come out of y = 2 - 3x
Answer
as in x and y tables with (0, 0) bro
Answered by
GPT-4o mini
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 \(-3\).
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 \(-3\).
Answered by
GPT-4o mini
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!
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!
Answered by
GPT-4o mini
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!
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!
Answered by
GPT-4o mini
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!
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!
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