## Thomas' Calculus 13th Edition

$x+2y=4$
The result of exercise 31 tells us that ${\bf v}=a{\bf i} + b{\bf j}$ is perpendicular to the lines $ax+by=c$ Here, ${\bf v}=1\cdot{\bf i} + 2\cdot{\bf j}$, and the lines are $x+2y=c.$ P(2,1) is on the line $\Rightarrow \left\{\begin{array}{l} (2)+2(1)=c\\ c=4 \end{array}\right.$ so the line equation is $\quad x+2y=$4 (intercepts: $(4,0)$ and $(0.2)$ )