Find the slope of a line parallel to the line which passes through the points:
(-a, 0) and (0, b)

Answer

To find the slope of a line parallel to the line that passes through the points (-a, 0) and (0, b), we can follow these steps:

### Step 1: Identify the coordinates of the points
Let point A be (-a, 0) and point B be (0, b).

### 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:
\[ m = \frac{y2 - y1}{x2 - x1} \]
In our case, we have:
- \(x1 = -a\), \(y1 = 0\)
- \(x2 = 0\), \(y2 = b\)

### Step 3: Substitute the coordinates into the slope formula
Substituting the coordinates into the slope formula, we get:
\[ m_{AB} = \frac{b - 0}{0 - (-a)} = \frac{b}{a} \]

### Step 4: State the property of parallel lines
We know that the slopes of parallel lines are equal. Therefore, the slope of any line parallel to line AB will also be \(\frac{b}{a}\).

### Step 5: Conclusion
Thus, the slope of the line parallel to the line passing through the points (-a, 0) and (0, b) is:
\[ \text{Required slope} = \frac{b}{a} \]

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