1. **State the problem:** We need to find the equation of the line passing through points such as $(-9,-9)$, $(-6,-6)$, $(0,0)$, $(3,3)$, $(6,6)$, $(9,9)$, and $(12,12)$ in slope-intercept form $y=mx+b$. 2. **Recall the slope-intercept form:** The equation of a line is given by $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope is the change in $y$ divided by the change in $x$ between any two points. Using points $(-9,-9)$ and $(-6,-6)$: $$m=\frac{-6 - (-9)}{-6 - (-9)}=\frac{-6 + 9}{-6 + 9}=\frac{3}{3}=1$$ 4. **Find the y-intercept $b$:** Since the line passes through $(0,0)$, substitute $x=0$ and $y=0$ into $y=mx+b$: $$0=1\times 0 + b \implies b=0$$ 5. **Write the final equation:** $$y=1x+0$$ which simplifies to $$y=x$$ **Answer:** The equation of the line in slope-intercept form is $y=x$.