**Calculating Slope :**

In this section, we are going to learn, how to calculate slope of a line, if two points on the line are given.

Let (x_{1}, y_{1}) and (x_{2}, y_{2}) be the two points on a line.

Then, the formula shown below can be used to calculate slope of the line

**Example 1 : **

Find the slope of a line passing through (3, -9) and (2, -1).

**Solution :**

Formula for slope :

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

Substitute (x_{1}, y_{1}) = (3, -9) and (x_{2}, y_{2}) = (2, -1).

m = [-1 - (-9)] / (2 - 3)

m = (-1 + 9) / (2 - 3)

m = 8 / (-1)

m = -8

So, the slope of the line is -8.

**Example 2 : **

Find the slope of a line passing through (3, 6) and (4, 1).

**Solution :**

Formula for slope :

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

Substitute (x_{1}, y_{1}) = (3, 6) and (x_{2}, y_{2}) = (4, 1).

m = (1 - 6) / (4 - 3)

m = (-5) / 1

m = -5

So, the slope of the line is -5.

**Example 3 : **

Find the slope of a line passing through (7, -3) and (0, -4).

**Solution :**

Formula for slope :

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

Substitute (x_{1}, y_{1}) = (7, -3) and (x_{2}, y_{2}) = (0, -4).

m = [-4 - (-3)] / (0 - 7)

m = (-4 + 3) / (-7)

m = (-1) / (-7)

m = 1 / 7

So, the slope of the line is 1/7.

**Example 4 : **

If the slope of a line joining (2, -6) and (8, k) is 2, find the value of k.

**Solution :**

Formula for slope :

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

Substitute m = 2, (x_{1}, y_{1}) = (2, -6) and (x_{2}, y_{2}) = (8, k).

2 = [k - (-6)] / (8 - 2)

2 = (k + 6) / 6

Multiply each side by 6.

12 = k + 6

Subtract 6 from each side.

6 = k

So, the value of k is 6.

**Example 5 : **

If the slope of a line joining (0, k) and (3, -15) is -6, find the value of k.

**Solution :**

Formula for slope :

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

Substitute m = -6, (x_{1}, y_{1}) = (0, k) and (x_{2}, y_{2}) = (3, -15).

-6 = (-15 - k) / (3 - 0)

-6 = (-15 - k) / 3

Multiply each side by 3.

-18 = -15 - k

Add 15 to each side.

-3 = -k

Multiply each side by -1

3 = k

So, the value of k is 3.

**Example 6 : **

If the slope of a line joining (k, 3) and (4, 8 ) is 5/6, find the value of k.

**Solution :**

Formula for slope :

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

Substitute m = 5/6, (x_{1}, y_{1}) = (k, 3) and (x_{2}, y_{2}) = (4, 8).

5/6 = (8 - 3) / (4 - k)

5/6 = 5 / (4 - k)

Cross multiply.

5(4 - k) = 5 ⋅ 6

Simplify.

20 - 5k = 30

Subtract 20 from each side.

-5k = 10

Divide each side by -5.

k = -2

So, the value of k is -2.

After having gone through the stuff given above, we hope that the students would have understood, "Calculating Slope".

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