To find the equation of a line in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept, we can use the point-slope form of the equation:
\[ y - y_1 = m(x - x_1) \]
Given:
- The point \( (x_1, y_1) = (6, 13) \)
- The slope \( m = -2 \)
Substituting these values into the point-slope form:
\[ y - 13 = -2(x - 6) \]
Now, simplify the equation:
\[ y - 13 = -2x + 12 \]
Next, add 13 to both sides to isolate \( y \):
\[ y = -2x + 12 + 13 \]
\[ y = -2x + 25 \]
So, the equation of the line in slope-intercept form is:
\[ y = -2x + 25 \]