Answer
a) $x+4y=1$
b) $ x=1$
$ y=\dfrac{1}{4}$
and $z$-intercept$=\infty$
Work Step by Step
a) The plane containing the point $P(1,0,-9)$ and having the normal vector $n=i+4j=\lt 1,4,0 \gt$ is expressed algebraically by the equation as follows:
$1(x-1) +4(y-0)+0(z-(-9))=0$
or, $x-1+4y=0 \implies x+4y=1$
b) To find the $x$-intercept, let us consider $y=0$
Thus, $x+0=1\implies x=1$
To find the $y$-intercept, let us consider $x=z=0$
Thus, $0+4y=1 \implies y=\dfrac{1}{4}$
and the $z$-intercept$=\infty$
