What is the slope of the line per allel to the line passing through the points (5, -1) and (4, -4) ?

Options

A. `-3`
B. `-(1)/(3)`
C. 3
D. `(1)/(3)`

Answer

To find the slope of the line parallel to the line passing through the points (5, -1) and (4, -4), we need to follow these steps:

### Step 1: Identify the Coordinates
We have two points:
- Point 1: (5, -1) which we will denote as (x₁, y₁)
- Point 2: (4, -4) which we will denote as (x₂, y₂)

### Step 2: Use the Slope Formula
The formula for the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
\[ m = \frac{y₂ - y₁}{x₂ - x₁} \]

### Step 3: Substitute the Values
Now, we will substitute the values into the slope formula:
- y₂ = -4
- y₁ = -1
- x₂ = 4
- x₁ = 5

Substituting these values, we get:
\[ m = \frac{-4 - (-1)}{4 - 5} \]

### Step 4: Simplify the Expression
Now, simplify the expression:
\[ m = \frac{-4 + 1}{4 - 5} \]
\[ m = \frac{-3}{-1} \]

### Step 5: Calculate the Slope
Now, we can calculate the slope:
\[ m = 3 \]

### Step 6: Conclusion
Since parallel lines have the same slope, the slope of the line parallel to the line passing through the points (5, -1) and (4, -4) is **3**.