Answer
Here is the completed table of values for the equation \( y = 4x - 2 \):
| \( x \) | \( y \) |
|:-------:|:-------:|
| -3 | -14 |
| -2 | -10 |
| -1 | -6 |
| 0 | -2 |
| 1 | 2 |
| 2 | 6 |
| 3 | 10 |
Solution
Certainly! Let's create and complete a table of values for the linear equation \( y = 4x - 2 \). This table will show corresponding \( y \) values for selected \( x \) values.
### (a) Table of Values for \( y = 4x - 2 \)
| \( x \) | \( y = 4x - 2 \) |
|:-------:|:---------------:|
| -3 | \( 4(-3) - 2 = -12 - 2 = -14 \) |
| -2 | \( 4(-2) - 2 = -8 - 2 = -10 \) |
| -1 | \( 4(-1) - 2 = -4 - 2 = -6 \) |
| 0 | \( 4(0) - 2 = 0 - 2 = -2 \) |
| 1 | \( 4(1) - 2 = 4 - 2 = 2 \) |
| 2 | \( 4(2) - 2 = 8 - 2 = 6 \) |
| 3 | \( 4(3) - 2 = 12 - 2 = 10 \) |
### Explanation:
1. **Choose \( x \)-values:** Select a range of \( x \)-values for which you want to find the corresponding \( y \)-values. In this case, we've chosen \( x = -3, -2, -1, 0, 1, 2, 3 \).
2. **Apply the equation:** For each \( x \)-value, substitute it into the equation \( y = 4x - 2 \) to compute \( y \).
- **Example Calculation for \( x = 2 \):**
\[
y = 4(2) - 2 = 8 - 2 = 6
\]
3. **Complete the table:** Fill in each row with the corresponding \( y \)-value calculated from the equation.
### Visual Representation:
Here's how the table looks with all values filled in:
| \( x \) | \( y \) |
|:-------:|:-------:|
| -3 | -14 |
| -2 | -10 |
| -1 | -6 |
| 0 | -2 |
| 1 | 2 |
| 2 | 6 |
| 3 | 10 |
### Plotting the Points (Optional)
If you plot these points on a coordinate plane, you'll notice they form a straight line, which is characteristic of linear equations. The slope of the line is 4, and the y-intercept is -2.
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Feel free to choose different \( x \)-values to explore how \( y \) changes accordingly!
Reviewed and approved by the UpStudy tutoring team
Explain
Simplify this solution
