Point Slope Equation 790Ff4

1. **State the problem:** We need to find the point-slope form of a line passing through the point $(-2, 4)$ with slope $3$. 2. **Recall the point-slope formula:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute the given point and slope:** Here, $x_1 = -2$, $y_1 = 4$, and $m = 3$. Substituting these values gives: $$y - 4 = 3(x - (-2))$$ which simplifies to: $$y - 4 = 3(x + 2)$$ 4. **Compare with the options:** - Option A: $y - 2 = 3(x - 4)$ (incorrect point values) - Option B: $y - 4 = 3(x - 2)$ (incorrect $x$ value) - Option C: $y + 2 = 3(x - 4)$ (incorrect signs and values) - Option D: $y - 4 = 3(x + 2)$ (matches our derived equation) 5. **Conclusion:** The correct point-slope equation is option D. **Final answer:** D. $y - 4 = 3(x + 2)$