1. **State the problem:** Find the equation of a line in slope-intercept form $y=mx+b$ that passes through the point $(5,5)$ with slope $m=-\frac{2}{7}$. 2. **Recall the slope-intercept form:** The equation of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Use the point-slope form to find $b$:** Substitute $m=-\frac{2}{7}$ and point $(x_1,y_1)=(5,5)$ into $y=mx+b$: $$5 = -\frac{2}{7} \times 5 + b$$ 4. **Calculate:** $$5 = -\frac{10}{7} + b$$ 5. **Solve for $b$:** $$b = 5 + \frac{10}{7} = \frac{35}{7} + \frac{10}{7} = \frac{45}{7}$$ 6. **Write the final equation:** $$y = -\frac{2}{7}x + \frac{45}{7}$$ 7. **Check the options:** None of the options match $b=\frac{45}{7}$. The given options have $b=\pm \frac{2}{7}$, so none are correct based on the point and slope. **Final answer:** The correct slope-intercept form is $$y = -\frac{2}{7}x + \frac{45}{7}$$ which is not listed among the options.