The value of 'p' such that the line passing through the points `(-4,p)and (1,3)` is parallel to the line passing through the points `(-2,5)and (8,7)` is

Options

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

Answer

To find the value of 'p' such that the line passing through the points (-4, p) and (1, 3) is parallel to the line passing through the points (-2, 5) and (8, 7), we need to follow these steps:

### Step 1: Find the slope of the line passing through the points (-2, 5) and (8, 7).

The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:
\[ m = \frac{y2 - y1}{x2 - x1} \]

For the points (-2, 5) and (8, 7):
- \(x_1 = -2\), \(y_1 = 5\)
- \(x_2 = 8\), \(y_2 = 7\)

Substituting the values:
\[ m = \frac{7 - 5}{8 - (-2)} = \frac{2}{8 + 2} = \frac{2}{10} = \frac{1}{5} \]

### Step 2: Set up the slope of the line passing through the points (-4, p) and (1, 3).

Using the same slope formula for the points (-4, p) and (1, 3):
- \(x_1 = -4\), \(y_1 = p\)
- \(x_2 = 1\), \(y_2 = 3\)

The slope is:
\[ m = \frac{3 - p}{1 - (-4)} = \frac{3 - p}{1 + 4} = \frac{3 - p}{5} \]

### Step 3: Set the slopes equal to each other since the lines are parallel.

Since the lines are parallel, their slopes must be equal:
\[ \frac{3 - p}{5} = \frac{1}{5} \]

### Step 4: Solve for 'p'.

To eliminate the fraction, we can multiply both sides by 5:
\[ 3 - p = 1 \]

Now, isolate 'p':
\[ -p = 1 - 3 \]
\[ -p = -2 \]
\[ p = 2 \]

### Conclusion:
The value of 'p' such that the line passing through the points (-4, p) and (1, 3) is parallel to the line passing through the points (-2, 5) and (8, 7) is:
\[ \boxed{2} \]