The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :
the equation of AB.

Answer

To find the equation of the line AB given the coordinates of points A and B, we can follow these steps:

### Step 1: Identify the coordinates of points A and B
- Point A has coordinates (-3, 4).
- Point B has coordinates (2, -1).

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

Here, we can assign:
- \( x1 = -3 \), \( y1 = 4 \) (for point A)
- \( x2 = 2 \), \( y2 = -1 \) (for point B)

### Step 3: Substitute the values into the gradient formula
Substituting the values into the formula:
\[ m = \frac{-1 - 4}{2 - (-3)} \]
\[ m = \frac{-5}{2 + 3} \]
\[ m = \frac{-5}{5} \]
\[ m = -1 \]

### Step 4: Use the point-slope form of the equation of a line
The point-slope form of the equation of a line is:
\[ y - y1 = m(x - x1) \]

We can use point A (-3, 4) for this equation:
\[ y - 4 = -1(x - (-3)) \]
\[ y - 4 = -1(x + 3) \]

### Step 5: Simplify the equation
Distributing the -1:
\[ y - 4 = -x - 3 \]
Now, add 4 to both sides:
\[ y = -x - 3 + 4 \]
\[ y = -x + 1 \]

### Final Equation
The equation of the line AB is:
\[ y = -x + 1 \]

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