1. **State the problem:** We need to find the values of $m$ (slope) and $c$ (y-intercept) for the line $R$ given by the equation $y = mx + c$. 2. **Identify given points:** The line passes through points $(0, -4)$ and $(2, 2)$. 3. **Find the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (0, -4)$ and $(x_2, y_2) = (2, 2)$. 4. **Calculate slope:** $$m = \frac{2 - (-4)}{2 - 0} = \frac{2 + 4}{2} = \frac{6}{2} = 3$$ 5. **Find the y-intercept $c$:** Since the line crosses the y-axis at $(0, -4)$, the y-intercept is $c = -4$. 6. **Write the equation:** Substitute $m = 3$ and $c = -4$ into $y = mx + c$ to get $$y = 3x - 4$$ **Final answer:** $m = 3$ and $c = -4$