## Linear Algebra: A Modern Introduction

Normal form of the equation of the line is:$\begin{bmatrix}{3 \\-4}\end{bmatrix} \cdot \begin{bmatrix}{x \\y}\end{bmatrix}=-5$; General form of the equation of the line is: $3x-4y=-5$
The normal form of a line is: $n \cdot (x-p)=0$ and $n=\begin{bmatrix}{a \\b}\end{bmatrix}$ Here, $a=3, b=-4$ The normal form of the line is:$\begin{bmatrix}{3 \\-4}\end{bmatrix} \cdot \begin{bmatrix}{x \\y}\end{bmatrix}=-5$ The general form of the equation of the line is: $ax+by=c$ Thus, the general form of the equation of the line is: $3x-4y=c$ or, $3(1)-4(2)=c \implies c=-5$ Hence, the normal form of the line is:$\begin{bmatrix}{3 \\-4}\end{bmatrix} \cdot \begin{bmatrix}{x \\y}\end{bmatrix}=-5$; The general form of the equation of the line is: $3x-4y=-5$