The slope of the line passing through the points ( 2, - 1) and (x, 5) is - 1 . Find x ?

Options

A. 4
B. `-4`
C. `-8`
D. 8

Answer

To find the value of \( x \) such that the slope of the line passing through the points \( (2, -1) \) and \( (x, 5) \) is \( -1 \), we will use the formula for the slope of a line, which is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 1: Identify the points and the slope
We have the points:
- \( (x_1, y_1) = (2, -1) \)
- \( (x_2, y_2) = (x, 5) \)

The slope \( m \) is given as \( -1 \).

### Step 2: Substitute the values into the slope formula
Using the slope formula, we can substitute the values we have:

\[ -1 = \frac{5 - (-1)}{x - 2} \]

### Step 3: Simplify the equation
Now, simplify the numerator:

\[ -1 = \frac{5 + 1}{x - 2} \]
\[ -1 = \frac{6}{x - 2} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiply to solve for \( x \):

\[ -1 \cdot (x - 2) = 6 \]
\[ -x + 2 = 6 \]

### Step 5: Solve for \( x \)
Now, isolate \( x \):

\[ -x = 6 - 2 \]
\[ -x = 4 \]
\[ x = -4 \]

### Conclusion
Thus, the value of \( x \) is \( -4 \).