**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".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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