Choice C is correct. An equation of a line can be written in the form $y=mx+b$, where $m$ is the slope of the line and $\left(0,b\right)$ is the y-intercept of the line. The line shown passes through the point $\left(0,-8\right)$, so $b=-8$. The line shown also passes through the point $\left(-8,0\right)$. The slope, $m$, of a line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ can be calculated using the equation $m=\frac{y_2-y_1}{x_2-x_1}$. For the points $\left(0,-8\right)$ and $\left(-8,0\right)$, this gives $m=\frac{\left(-8\right)-0}{0-\left(-8\right)}$, or $m=-1$. Substituting $-8$ for $b$ and $-1$ for $m$ in $y=mx+b$ yields $y=\left(-1\right)x+\left(-8\right)$, or $y=-x-8$. Therefore, an equation of the graph shown is $y=-x-8$.

Choice A is incorrect. This is an equation of a line with a slope of $-2$, not $-1$.

Choice B is incorrect. This is an equation of a line with a slope of $1$, not $-1$.

Choice D is incorrect. This is an equation of a line with a slope of $2$, not $-1$.