To find the standard form of the equation of the line going through the points in the table, we can first determine the slope (m) from the given points and then use the point-slope form of the equation.
From the values provided:
- Two points we can choose are (3, 6) and (6, 4).
To find the slope (m):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 6}{6 - 3} = \frac{-2}{3} \]
Using the point-slope form of the equation of a line, \(y - y_1 = m(x - x_1)\), we can plug in one of the points and the slope:
Using the point (3, 6):
\[ y - 6 = -\frac{2}{3}(x - 3) \]
Now, we can convert this to standard form (Ax + By = C).
- Distributing the slope on the right side:
\[ y - 6 = -\frac{2}{3}x + 2 \]
- Adding 6 to both sides:
\[ y = -\frac{2}{3}x + 8 \]
- To convert to standard form, we can multiply everything by 3 to eliminate the fraction:
\[ 3y = -2x + 24 \]
Rearranging gives us:
\[ 2x + 3y = 24 \]
So, the correct answer confirming the standard form of the equation of the line is:
\[ 2x + 3y = 24 \]
The correct response is:
2x + 3y = 24.