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 solve the problem, we need to find the value of \( x \) given that the slope of the line containing the points \( (2, 5) \) and \( (x, -4) \) is 3.

### Step-by-Step Solution:

1. **Understanding the Slope Formula**:
The slope \( m \) of a line through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we have the points \( (2, 5) \) and \( (x, -4) \).

2. **Assigning the Points**:
Let \( (x_1, y_1) = (2, 5) \) and \( (x_2, y_2) = (x, -4) \).

3. **Substituting into the Slope Formula**:
We know the slope \( m = 3 \). So, substituting the values into the slope formula:
\[ 3 = \frac{-4 - 5}{x - 2} \]

4. **Simplifying the Equation**:
Now, simplify the numerator:
\[ -4 - 5 = -9 \]
Thus, the equation becomes:
\[ 3 = \frac{-9}{x - 2} \]

5. **Cross-Multiplying**:
To eliminate the fraction, we can cross-multiply:
\[ 3(x - 2) = -9 \]

6. **Distributing**:
Distributing the 3 on the left side:
\[ 3x - 6 = -9 \]

7. **Solving for \( x \)**:
Now, add 6 to both sides:
\[ 3x = -9 + 6 \]
\[ 3x = -3 \]
Now, divide by 3:
\[ x = -1 \]

### Final Answer:
The value of \( x \) is \( -1 \).

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