table of values:

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

3 answers

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!

what linear equation does the table represent?

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.

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