x and y values

To find the standard form of the equation of the line that goes through the points given in the table, we need to determine the slope (m) and the y-intercept (b) from the coordinates (x, y). The points from the table are:

• (0, 8)
• (3, 6)
• (6, 4)
• (9, 2)
• (12, 0)

Step 1: Calculate the slope (m)

The slope \( m \) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (0, 8) and (3, 6):

\[ m = \frac{6 - 8}{3 - 0} = \frac{-2}{3} \]

Step 2: Write the equation in slope-intercept form (y = mx + b)

Now that we have the slope, we can use one of the points to find the intercept \( b \). We can use the point (0, 8):

\[ 8 = \left(-\frac{2}{3}\right)(0) + b \] \[ b = 8 \]

Thus, the equation of the line in slope-intercept form is:

\[ y = -\frac{2}{3}x + 8 \]

Step 3: Convert to standard form (Ax + By = C)

To convert from slope-intercept form to standard form, we will rearrange the equation:

1. Start with: \( y = -\frac{2}{3}x + 8 \)
2. Multiply through by 3 to eliminate the fraction: \[ 3y = -2x + 24 \]
3. Rearrange into standard form: \[ 2x + 3y = 24 \]

Conclusion

The standard form of the equation of the line going through the points in the table is:

\[ \boxed{2x + 3y = 24} \]