**How to prove if the given points are collinear using slope :**

The points which lies on the same line is known as collinear points.

In case we have three point and we need to prove that the given points are collinear, we may follow the steps given below.

Working Rule :

**Step 1 :**

Choose the points A and B and find the slope.

**Step 2 :**

Choose the points B and C and find the slope.

**Step 3 :**

If the slopes from step 1 and step 2 are equal, we may say the given points are collinear.

m = (y_{2} - y_{1})/(x_{2}-x_{1})

**Example 1 :**

Using the concept of slope, show that each of the following set of points are collinear.

(2 , 3), (3 , -1) and (4 , -5)

**Solution :**

Formula to find the slope of the line passing through two points

m = (y_{2} - y_{1})/(x_{2}-x_{1})

**Step 1 :**

**Slope of AB :**

(x_{1}, y_{1}) ==> (2, 3) and (x_{2}, y_{2}) ==> (3, -1)

m = (-1 - 3) / (3 - 2)

= (-4 )/1

= -4

**Step 2 :**

**Slope of BC :**

(x_{1}, y_{1}) ==> (3 , -1) and (x_{2}, y_{2}) ==> (4, -5)

m = (-5 - (-1)) / (4 - 3)

= (-5 + 1 )/1

= -4

**Step 3 :**

Slope of AB = Slope of BC

Hence the given points are collinear.

**Example 2 :**

Using the concept of slope, show that each of the following set of points are collinear.

(4 , 4), (-2 , 6) and (1 , 5)

**Solution :**

Formula to find the slope of the line passing through two points

m = (y_{2} - y_{1})/(x_{2}-x_{1})

**Step 1 :**

**Slope of AB :**

(x_{1}, y_{1}) ==> (4 , 4) and (x_{2}, y_{2}) ==> (-2 , 6)

m = (6 - 4) / (-2 - 4)

= 2/(-6)

= -1/3

**Step 2 :**

**Slope of BC :**

(x_{1}, y_{1}) ==> (-2, 6) and (x_{2}, y_{2}) ==> (1, 5)

m = (5 - 6) / (1 - (-2))

= (-1 )/(1 + 2)

= -1/3

**Step 3 :**

Slope of AB = Slope of BC

Hence the given points are collinear.

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