Answer
$3x+2y=7$ or, $3x-+2y-7=0$
$ x=\dfrac{7}{3}$
and $y=\dfrac{7}{2}$
Work Step by Step
The plane containing the point $P(3,2,0)$ and having the normal vector $n=\lt 1,2,7\gt$ is expressed algebraically by the equation as follows:
$3(x-1)+2(y-2)+0(z-7)=0$
or, $3x-3+2y-4=0 \implies 3x+2y=7$ or, $3x-+2y-7=0$
To find the $x$-intercept, let us consider $y=0$
Thus, $3x+0=7 \implies x=\dfrac{7}{3}$
To find the $y$-intercept, let us consider $x=0$
Thus, $0+2y=7 \implies y=\dfrac{7}{2}$
