If the slope of the line containg the point (2,5) and (x, - 4) is 3, then the value of x is :

Options

A. 3
B. 1
C. 2
D. `-1`

Answer

To find the value of \( x \) given that the slope of the line containing the points \( (2, 5) \) and \( (x, -4) \) is 3, we can follow these steps:

### Step 1: Write the formula for the slope of a line
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 2: Substitute the given points into the slope formula
Here, we have the points \( (2, 5) \) and \( (x, -4) \). So, we can substitute:
- \( x_1 = 2 \)
- \( y_1 = 5 \)
- \( x_2 = x \)
- \( y_2 = -4 \)

Substituting these into the slope formula gives:
\[ 3 = \frac{-4 - 5}{x - 2} \]

### Step 3: Simplify the equation
Now, simplify the numerator:
\[ -4 - 5 = -9 \]
So the equation becomes:
\[ 3 = \frac{-9}{x - 2} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 3(x - 2) = -9 \]

### Step 5: Distribute the 3
Distributing the 3 on the left side:
\[ 3x - 6 = -9 \]

### Step 6: Solve for \( x \)
Now, add 6 to both sides:
\[ 3x = -9 + 6 \]
\[ 3x = -3 \]
Now, divide by 3:
\[ x = -1 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{-1} \]