11) $$ (-5,-2) $$ and $$ (x, 6) $$; slope: $$ \frac{8}{3} $$

Question

UpStudy AI · Accepted Answer

To find the value of $$ x $$ given the two points $$(-5, -2)$$ and $$(x, 6)$$ with a slope of $$ \frac{8}{3} $$, we'll use the **slope formula**:

$$
\text{Slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}
$$

**Given:**
- Point 1: $$(x_1, y_1) = (-5, -2)$$
- Point 2: $$(x_2, y_2) = (x, 6)$$
- Slope: $$ m = \frac{8}{3} $$

**Step-by-Step Solution:**

1. **Plug the known values into the slope formula:**

$$
\frac{8}{3} = \frac{6 - (-2)}{x - (-5)}
$$

2. **Simplify the numerator and the denominator:**

$$
\frac{8}{3} = \frac{6 + 2}{x + 5} \
\frac{8}{3} = \frac{8}{x + 5}
$$

3. **Set up the equation:**

$$
\frac{8}{3} = \frac{8}{x + 5}
$$

4. **Cross-multiply to eliminate the fractions:**

$$
8 \cdot (x + 5) = 8 \cdot 3
$$

5. **Simplify both sides:**

$$
8x + 40 = 24
$$

6. **Solve for $$ x $$:**

$$
8x = 24 - 40 \
8x = -16 \
x = \frac{-16}{8} \
x = -2
$$

**Answer:** $$ x = -2 $$
$$ x = -2 $$

and ; slope: