1. **State the problem:** We need to find the equation of a line with slope $-4$ passing through the point $(2,-15)$ in slope-intercept form $y=mx+b$. 2. **Recall the slope-intercept form:** The equation of a line is given by $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Use the point-slope form to find $b$:** Substitute $m=-4$, $x=2$, and $y=-15$ into the equation: $$-15 = -4(2) + b$$ 4. **Simplify and solve for $b$:** $$-15 = -8 + b$$ Add 8 to both sides: $$-15 + 8 = b$$ $$b = -7$$ 5. **Write the final equation:** $$y = -4x - 7$$ This is the equation of the line in slope-intercept form with integer coefficients.