We need to find the slope and $$ y$$-intercept of the line from the graph so we can substitute the needed values into the slope-intercept form, $y=mx+b$.

To find the slope, we choose two points on the graph.

The $$ y$$-intercept is $(\text{}0\text{},\text{}-3\text{})$ and the graph passes through $(\text{}3\text{},\text{}-4\text{})$.

Find the slope by counting the rise and run.

$m=\frac{\mathrm{rise}}{\mathrm{run}}$

$m=\frac{\text{-1}}{3}$

Find the $$ y$$-intercept.

$y\text{-intercept}\text{}\text{\hspace{0.17em}=\hspace{0.17em}}\text{}\text{(\hspace{0.17em}}\text{}0\text{}\text{\hspace{0.17em},\hspace{0.17em}}\text{}-3\text{}\text{\hspace{0.17em})}$

Substitute the values into $y=mx+b$.

$y\text{}\text{\hspace{0.17em}=\hspace{0.17em}}\text{}m\text{}\text{}x\text{}\text{\hspace{0.17em}+\hspace{0.17em}}\text{}b$

$y=-\frac{1}{3}x+\left(-3\right)$

$y=-\frac{1}{3}\text{}x-3$