1. **State the problem:** Find the equation of the line in slope-intercept form $y=mx+b$ that passes through the point $(-5,4)$ with slope $m=3$. 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 $m=3$, $x=-5$, and $y=4$ into the equation: $$4=3(-5)+b$$ 4. **Simplify and solve for $b$:** $$4 = -15 + b$$ Add 15 to both sides: $$4 + 15 = b$$ $$b = 19$$ 5. **Write the final equation:** $$y = 3x + 19$$ 6. **Check the options:** The correct choice is D. $y=3x+19$. This is the equation of the line passing through $(-5,4)$ with slope 3 in slope-intercept form.