To write the equation of a line in standard form, we can start with the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is a point on the line, and \(m\) is the slope.
Given:
- The point \((x_1, y_1) = (2, 9)\)
- The slope \(m = \frac{1}{2}\)
Substituting these values into the point-slope form:
\[ y - 9 = \frac{1}{2}(x - 2) \]
Now, we can simplify this equation:
- Distributing the slope on the right side:
\[ y - 9 = \frac{1}{2}x - 1 \]
- Adding 9 to both sides to isolate \(y\):
\[ y = \frac{1}{2}x + 8 \]
Now, we need to convert this equation into standard form, which is \(Ax + By = C\) where \(A\), \(B\), and \(C\) are integers, and \(A\) should be non-negative.
Starting with:
\[ y = \frac{1}{2}x + 8 \]
We can multiply every term by 2 to eliminate the fraction:
\[ 2y = x + 16 \]
Now, rearranging this to standard form:
\[ -x + 2y = 16 \]
To write it in the standard form \(Ax + By = C\) with \(A\) being positive, we multiply the entire equation by -1:
\[ x - 2y = -16 \]
Thus, the equation of the line in standard form is:
\[ x - 2y = -16 \]
So, the final answer in standard form is:
\[ x - 2y = -16 \]