The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :
the equation of PQ

Answer

To find the equation of the line passing through the points P(2, 6) and Q(-3, 5), we will follow these steps:

### Step 1: Identify the coordinates of the points
The coordinates of point P are (2, 6) and the coordinates of point Q are (-3, 5).

### Step 2: Use the formula for the equation of a line
The formula for the equation of a line through two points (x₁, y₁) and (x₂, y₂) is given by:

\[ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} \]

Here, we will assign:
- \(x_1 = 2\), \(y_1 = 6\) (for point P)
- \(x_2 = -3\), \(y_2 = 5\) (for point Q)

### Step 3: Substitute the coordinates into the formula
Substituting the values into the formula, we get:

\[ \frac{y - 6}{5 - 6} = \frac{x - 2}{-3 - 2} \]

### Step 4: Simplify the equation
Calculating the differences:
- \(5 - 6 = -1\)
- \(-3 - 2 = -5\)

So the equation becomes:

\[ \frac{y - 6}{-1} = \frac{x - 2}{-5} \]

### Step 5: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:

\[ -5(y - 6) = -1(x - 2) \]

### Step 6: Distribute and simplify
Distributing both sides:

\[ -5y + 30 = -x + 2 \]

Rearranging gives:

\[ x - 5y + 30 - 2 = 0 \]

This simplifies to:

\[ x - 5y + 28 = 0 \]

### Final Equation
Thus, the equation of the line PQ is:

\[ x - 5y + 28 = 0 \]

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