For a line given by \( Ax + By = C \), the slope is:
\[ m = -\frac{A}{B} \quad (B \neq 0) \]Parallel lines have equal slopes. Using point-slope form:
\[ y - y_0 = m(x - x_0) \]This simplifies to slope-intercept form \( y = mx + b \).
If \( B = 0 \), the given line is vertical (\( x = \text{constant} \)), and the parallel line through the point is \( x = x_0 \).