1. The problem is to find the equation of a line that passes through the point $(-2,7)$ and has a slope of $4$. 2. Recall the point-slope form of a line: $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. Substitute $m = 4$ and $(x_1, y_1) = (-2,7)$ into the formula: $$y - 7 = 4(x - (-2))$$ which simplifies to: $$y - 7 = 4(x + 2)$$ 4. Distribute the $4$ on the right side: $$y - 7 = 4x + 8$$ 5. Add $7$ to both sides to solve for $y$: $$y = 4x + 8 + 7$$ $$y = 4x + 15$$ 6. Therefore, the equation of the line is $$y = 4x + 15$$. This line passes through $(-2,7)$ and has slope $4$ as required.