91Ó°ÊÓ

The slope intercept form of a straight-line equation is $y=mx+c$where $m$is the slope and $c$is the y-intercept.

The $x$-intercept is the value of $x$when $y=0$and the $y$-intercept is the value of $y$when $x=0$.

So, if the $x$-intercept is $a$, then the line passes through $\left(a,0\right)$ and if the $y$-intercept is $b$, then the line passes through $\left(0,b\right)$.

The equation of a straight-line passing through the points $\left(h,k\right)$ and $\left(a,b\right)$ is given as $\frac{y-k}{x-h}=\frac{b-k}{a-h}$.

It is given that the $x$-intercept is $-4$ and the $y$-intercept is $4$. Then, the line passes through $\left(-4,0\right)$ and $\left(0,4\right)$.

Then, $\left(h,k\right)=\left(-4,0\right)$ and $\left(a,b\right)=\left(0,4\right)$.

Put $\left(h,k\right)=\left(-4,0\right)$and $\left(a,b\right)=\left(0,4\right)$in $\frac{y-k}{x-h}=\frac{b-k}{a-h}$to get,

$\frac{y-0}{x-\left(-4\right)}=\frac{4-0}{0-\left(-4\right)}$

$\frac{y}{x+4}=\frac{4}{4}$ (Simplify)

$\frac{y}{x+4}=1$ (Simplify)

$\frac{y}{x+4}\left(x+4\right)=1\left(x+4\right)$ (Multiply both sides by $x+4$)

$y=x+4$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y=x+4$.