Example 1. Given the equation of a straight line $\frac{3 x-2}{4}-\frac{2 y-1}{2}=1$, find its

1) general equation;
2) slope-intercept equation;
3) intercept form equation
4) normal equation
Solution. 1) By bringing to a common denominator, we obtain the general equation of the line (point $1^{\circ}$) $3 x-4 y-4=0$.

2) From this, it is easy to obtain the equation of the line with the slope $y=\frac{3}{4} x-1$.
3) The equation in segments can be obtained from the general equation $3 x-4 y=4$ by term-by-term division by the free term: $\frac{x}{4 / 3}+\frac{y}{-1}=1$.
4) To obtain the normal equation, we find $\cos \varphi=$ $=\frac{A}{\sqrt{A^{2}+B^{2}}}=\frac{3}{\sqrt{9+16}}=\frac{3}{5} ; \quad \sin \varphi=\frac{B}{\sqrt{A^{2}+B^{2}}}=-\frac{4}{5}$ and $p=-\frac{C}{\sqrt{A^{2}+B^{2}}}=-\frac{-4}{5}=\frac{4}{5}$. Thus, $\frac{3}{5} x-\frac{4}{5} y-\frac{4}{5}=0-$ is the normal equation.