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

Answer

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

### Step 1: Write the formula for the slope
The formula for the slope \( m \) of a line passing through 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: Identify the points
Here, we have:
- Point 1: \( (x_1, y_1) = (x, 2) \)
- Point 2: \( (x_2, y_2) = (8, -11) \)

### Step 3: Substitute the points into the slope formula
Substituting the values into the slope formula, we get:
\[ -\frac{3}{4} = \frac{-11 - 2}{8 - x} \]

### Step 4: Simplify the expression
Calculating the numerator:
\[ -11 - 2 = -13 \]
So the equation becomes:
\[ -\frac{3}{4} = \frac{-13}{8 - x} \]

### Step 5: Eliminate the negative signs
Multiplying both sides by -1 gives:
\[ \frac{3}{4} = \frac{13}{8 - x} \]

### Step 6: Cross multiply
Cross multiplying gives:
\[ 3(8 - x) = 4 \cdot 13 \]
Calculating the right side:
\[ 4 \cdot 13 = 52 \]
So we have:
\[ 3(8 - x) = 52 \]

### Step 7: Distribute the 3
Distributing the 3 on the left side:
\[ 24 - 3x = 52 \]

### Step 8: Isolate the variable
Rearranging the equation to isolate \( x \):
\[ -3x = 52 - 24 \]
Calculating the right side:
\[ 52 - 24 = 28 \]
So we have:
\[ -3x = 28 \]

### Step 9: Solve for \( x \)
Dividing both sides by -3 gives:
\[ x = -\frac{28}{3} \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{-\frac{28}{3}} \]