1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ given the slope $m=-15$ and a point on the line $(-5,7)$. 2. **Recall the slope-intercept form:** The equation 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 $m=-15$, $x=-5$, and $y=7$ into $y=mx+b$: $$7 = (-15)(-5) + b$$ 4. **Calculate:** $$7 = 75 + b$$ 5. **Isolate $b$:** $$b = 7 - 75$$ $$b = -68$$ 6. **Write the final equation:** $$y = -15x - 68$$ This is the slope-intercept form of the line passing through $(-5,7)$ with slope $-15$.