1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ given the slope $m=1$ and a point $(-1,-7)$ on the line. 2. **Recall the formula:** The slope-intercept form is $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Substitute the slope:** We have $$y=1\cdot x + b$$ or simply $$y=x+b$$. 4. **Use the point to find $b$:** Substitute $x=-1$ and $y=-7$ into the equation: $$-7 = (-1) + b$$ 5. **Solve for $b$:** $$-7 = -1 + b$$ Add 1 to both sides: $$-7 + 1 = \cancel{-1} + b + 1$$ $$-6 = b$$ 6. **Write the final equation:** $$y = x - 6$$ This matches the given line passing through $(-1,-7)$ with slope 1. **Final answer:** $y = x - 6$