Question

x and y values
( x | 0 | 3 | 6 | 9 | 12 )
( y | 8 | 6 | 4 | 2 | 0 )

write the standard form of the equation of the lind going through the points in the table.

Answer 1

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:

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