To write the equation of the line in standard form, we start with the point-slope form of the line equation:
\[ y - y_1 = m(x - x_1) \]
Where \((x_1, y_1)\) is the point on the line and \(m\) is the slope. For your line:
- The point \((x_1, y_1)\) is \((2, 9)\)
- The slope \(m\) is \(\frac{1}{2}\)
Substituting these values into the point-slope form:
\[ y - 9 = \frac{1}{2}(x - 2) \]
Now, we simplify this equation:
\[ y - 9 = \frac{1}{2}x - 1 \]
Next, we'll add 9 to both sides:
\[ y = \frac{1}{2}x + 8 \]
Now, we'll convert this equation into standard form \(Ax + By = C\). First, multiply every term by 2 to eliminate the fraction:
\[ 2y = x + 16 \]
Next, rearrange the equation to the standard form \(Ax + By = C\):
\[ -x + 2y = 16 \]
To express this with a positive \(A\), we can multiply the entire equation by -1:
\[ x - 2y = -16 \]
Thus, the equation of the line in standard form is:
\[ x - 2y = -16 \]