1. **State the problem:** Find the equation of the line passing through the points $(-3,7)$ and $(0,0)$ in slope-intercept form $y=mx+b$. 2. **Recall the formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ The slope-intercept form is $$y=mx+b$$ where $b$ is the y-intercept. 3. **Calculate the slope:** Using points $(-3,7)$ and $(0,0)$, $$m=\frac{0 - 7}{0 - (-3)}=\frac{-7}{3}$$ 4. **Find the y-intercept $b$:** Since the line passes through $(0,0)$, the y-intercept is $$b=0$$ 5. **Write the equation:** Substitute $m$ and $b$ into the slope-intercept form: $$y = -\frac{7}{3}x + 0$$ which simplifies to $$y = -\frac{7}{3}x$$ **Final answer:** $$y = -\frac{7}{3}x$$