Question

How to create a table for the function y = 2x - 3?

Answer 1

To create a table for the function \( y = 2x - 3 \), you'll need to select a range of \( x \) values, calculate the corresponding \( y \) values using the function, and then present them in a table format.

Here’s a step-by-step guide:

1. **Choose a range of x values:** You can choose any range, but it often helps to pick negative, zero, and positive values to see how the function behaves. For example, we can use \( x = -2, -1, 0, 1, 2, 3 \).

2. **Calculate y values:** Substitute each \( x \) value into the function to find the corresponding \( y \) value.

3. **Create the table:** List the \( x \) values alongside their corresponding \( y \) values.

Here’s how it looks in detail:

### Step 1: Calculate \( y \) values

- For \( x = -2 \):
\[
y = 2(-2) - 3 = -4 - 3 = -7
\]
- For \( x = -1 \):
\[
y = 2(-1) - 3 = -2 - 3 = -5
\]
- For \( x = 0 \):
\[
y = 2(0) - 3 = 0 - 3 = -3
\]
- For \( x = 1 \):
\[
y = 2(1) - 3 = 2 - 3 = -1
\]
- For \( x = 2 \):
\[
y = 2(2) - 3 = 4 - 3 = 1
\]
- For \( x = 3 \):
\[
y = 2(3) - 3 = 6 - 3 = 3
\]

### Step 2: Create the table

Now, you can organize the \( x \) and \( y \) values into a table.

| \( x \) | \( y \) |
|---------|--------------|
| -2 | -7 |
| -1 | -5 |
| 0 | -3 |
| 1 | -1 |
| 2 | 1 |
| 3 | 3 |

This table shows the relationship between \( x \) and \( y \) for the function \( y = 2x - 3 \). You can use these values to plot the graph of the function or analyze its properties further!