The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :
the co-ordinates of the point where the line AB intersects the y-axis. 

Answer

To find the coordinates of the point where the line AB intersects the y-axis, we will follow these steps:

### Step 1: Identify the coordinates of points A and B
The coordinates of point A are \((-3, 4)\) and the coordinates of point B are \((2, -1)\).

### Step 2: Use the two-point form of the equation of a line
The two-point form of the equation of a line passing through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ \frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates of points A and B:
- \(x_1 = -3\), \(y_1 = 4\)
- \(x_2 = 2\), \(y_2 = -1\)

### Step 3: Substitute the values into the equation
\[ \frac{y - 4}{x + 3} = \frac{-1 - 4}{2 - (-3)} \]
Calculating the right side:
\[ \frac{-5}{5} = -1 \]

### Step 4: Set up the equation
Now we have:
\[ \frac{y - 4}{x + 3} = -1 \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ y - 4 = -1(x + 3) \]
This simplifies to:
\[ y - 4 = -x - 3 \]

### Step 6: Rearrange the equation
Rearranging gives:
\[ y + x + 1 = 0 \]
or
\[ x + y + 1 = 0 \]

### Step 7: Find the intersection with the y-axis
To find where the line intersects the y-axis, we set \(x = 0\):
\[ 0 + y + 1 = 0 \]
This simplifies to:
\[ y + 1 = 0 \implies y = -1 \]

### Step 8: Write the coordinates of the intersection point
Thus, the coordinates of the point where the line AB intersects the y-axis are \((0, -1)\).

### Final Answer:
The coordinates of the point where line AB intersects the y-axis are \((0, -1)\).

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