Find y if the slope of the line joining (-8, 11), (2, y) is `-4/(3)`.

Answer

To find the value of \( y \) given the slope of the line joining the points \((-8, 11)\) and \((2, y)\) is \(-\frac{4}{3}\), we can follow these steps:

### Step 1: Identify the points and the slope formula
Let the points be:
- Point A: \( (x_1, y_1) = (-8, 11) \)
- Point B: \( (x_2, y_2) = (2, y) \)

The formula for the slope \( m \) of a line joining two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 2: Substitute the known values into the slope formula
We know that the slope \( m \) is \(-\frac{4}{3}\). Substituting the values into the slope formula:
\[ -\frac{4}{3} = \frac{y - 11}{2 - (-8)} \]

### Step 3: Simplify the denominator
Calculate the denominator:
\[ 2 - (-8) = 2 + 8 = 10 \]
So, we can rewrite the equation as:
\[ -\frac{4}{3} = \frac{y - 11}{10} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ -4 \cdot 10 = 3(y - 11) \]
This simplifies to:
\[ -40 = 3(y - 11) \]

### Step 5: Distribute and isolate \( y \)
Distributing on the right side:
\[ -40 = 3y - 33 \]
Now, add 33 to both sides:
\[ -40 + 33 = 3y \]
This simplifies to:
\[ -7 = 3y \]

### Step 6: Solve for \( y \)
Now, divide both sides by 3:
\[ y = -\frac{7}{3} \]

### Conclusion
Thus, the value of \( y \) is:
\[ \boxed{-\frac{7}{3}} \]