*y*=*ax+ba*=−21.6285714286*b*=858.904761905 *create a table*

To create a table for the equation \( y = ax + b \), where \( a = -21.6285714286 \) and \( b = 858.904761905 \), we will generate a few values of \( x \) and compute the corresponding values of \( y \).

Let's choose a range of \( x \) values and calculate the corresponding \( y \) values:

| \( x \) | \( y = ax + b \) | \( y \) Value |
|:-------:|:---------------:|:-------------:|
|   -10   |   \( -21.6285714286(-10) + 858.904761905 \) |   \( 1075.190476191 \) |
|   -5    |   \( -21.6285714286(-5) + 858.904761905 \) |   \( 966.047619048 \)  |
|    0    |   \( -21.6285714286(0) + 858.904761905 \)  |   \( 858.904761905 \)  |
|    5    |   \( -21.6285714286(5) + 858.904761905 \)  |   \( 751.761904762 \)  |
|   10    |   \( -21.6285714286(10) + 858.904761905 \) |   \( 644.619047619 \)  |

### Summary of the Table

- When \( x = -10 \), \( y = 1075.190476191 \)
- When \( x = -5 \), \( y = 966.047619048 \)
- When \( x = 0 \), \( y = 858.904761905 \)
- When \( x = 5 \), \( y = 751.761904762 \)
- When \( x = 10 \), \( y = 644.619047619 \)

Would you like to explore more details or have any questions?

### Further Related Questions:
1. How does the slope \( a \) affect the steepness of the line?
2. What happens to the line when \( b \) changes?
3. How would the equation change if \( a \) were positive?
4. Can you find the \( x \)-intercept from this equation?
5. How does this linear function compare to a quadratic function?

### Tip:
When interpreting a linear equation, remember that \( a \) (the coefficient of \( x \)) represents the slope, which indicates how steep the line is, and \( b \) represents the y-intercept, where the line crosses the y-axis.

Learn how to create a table for the linear equation y = -21.63x + 858.90 with a step-by-step solution. This problem demonstrates the calculation of y values for various x values, highlighting the concept of linear equations. Suitable for students in Grades 7-9.

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