1. **State the problem:** We need to find the equation of the line passing through the points $(-4,-7)$ and $(1,7)$ in slope-intercept form, which is $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Find the slope $m$:** The slope formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)=(-4,-7)$ and $(x_2,y_2)=(1,7)$. Substitute values: $$m=\frac{7 - (-7)}{1 - (-4)}=\frac{7 + 7}{1 + 4}=\frac{14}{5}$$ 3. **Use the slope-intercept form $y=mx+b$ and substitute one point to find $b$:** Using point $(1,7)$: $$7=\frac{14}{5} \times 1 + b$$ $$7=\frac{14}{5} + b$$ 4. **Solve for $b$:** $$b=7 - \frac{14}{5}$$ Convert 7 to fraction with denominator 5: $$b=\frac{35}{5} - \frac{14}{5}=\frac{21}{5}$$ 5. **Write the final equation:** $$y=\frac{14}{5}x + \frac{21}{5}$$ This is the equation of the line in slope-intercept form.