Question

table of values:
x: y: yb:
0 3 18
1 6 13 1/2
2 9 9

Answer 1

what linear equation does the table represent?

Answer 2

It looks like you've provided a table with three columns: \( x \), \( y \), and \( yb \). Here’s the table formatted for clarity:

| \( x \) | \( y \) | \( yb \) |
|-----------|-----------|----------------|
| 0 | 3 | 18 |
| 1 | 6 | 13.5 |
| 2 | 9 | 9 |

If you have a specific question or need further analysis regarding this table or data, please let me know!

Answer 3

To determine the linear equations represented by the table of values, we can consider the pairs \((x, y)\) and \((x, yb)\) separately.

### For \(y\):

1. **Points from the table**:
- (0, 3)
- (1, 6)
- (2, 9)

2. **Finding the slope** (\(m\)):
Using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's calculate it using the first two points (0, 3) and (1, 6):
\[
m = \frac{6 - 3}{1 - 0} = \frac{3}{1} = 3
\]

3. **Finding the y-intercept** (\(b\)):
Using the slope-intercept form \(y = mx + b\).
When \(x = 0\), \(y = 3\), which gives us \(b = 3\).

4. **Putting it all together**:
The equation for \(y\) is:
\[
y = 3x + 3
\]

### For \(yb\):

1. **Points from the table**:
- (0, 18)
- (1, 13.5)
- (2, 9)

2. **Finding the slope** (\(m\)):
Let's calculate it using the first two points (0, 18) and (1, 13.5):
\[
m = \frac{13.5 - 18}{1 - 0} = \frac{-4.5}{1} = -4.5
\]

3. **Finding the y-intercept** (\(b\)):
When \(x = 0\), \(yb = 18\) which gives us \(b = 18\).

4. **Putting it all together**:
The equation for \(yb\) is:
\[
yb = -4.5x + 18
\]

### Summary of Equations:

- For \(y\):
\[
y = 3x + 3
\]

- For \(yb\):
\[
yb = -4.5x + 18
\]

These are the linear equations that represent the provided table of values.