Find Slope A 1B030C

1. **State the problem:** We need to find the value of $a$ such that the slope of the line segment $CD$ is $2$, given points $C(-3, -2)$ and $D(1, a)$. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Apply the formula to points $C$ and $D$:** $$2 = \frac{a - (-2)}{1 - (-3)} = \frac{a + 2}{1 + 3} = \frac{a + 2}{4}$$ 4. **Solve for $a$:** Multiply both sides by $4$ to isolate $a + 2$: $$4 \times 2 = a + 2$$ $$8 = a + 2$$ 5. **Subtract $2$ from both sides:** $$8 - 2 = a$$ $$6 = a$$ **Final answer:** $$a = 6$$