Answer
$a)$ $x$-intercept:$-6;$ $y$-intercept:$6$
$b)$ $x$-intercepts:$\pm\sqrt{5};$ $y$-intercept:$-5$
Work Step by Step
$a)$ $y=x+6$
To find the $x$-intercept, set $y$ equal to $0$ and solve for $x$:
$y=x+6$
$0=x+6$
$x=-6$
To find the $y$-intercept, set $x$ equal to $0$ and solve for $y$:
$y=x+6$
$y=0+6$
$y=6$
$b)$ $y=x^{2}-5$
To find the $x$-intercepts, set $y$ equal to $0$ and solve for $x$:
$y=x^{2}-5$
$0=x^{2}-5$
$x^{2}=5$
$x=\pm\sqrt{5}$
To find the $y$-intercept, set $x$ equal to $0$ and solve for $y$:
$y=x^{2}-5$
$y=(0)^{2}-5$
$y=-5$
