**Calculating slope m :**

When the rate of change of a relationship is constant, any segment of its graph has the same steepness. The constant rate of change is called the slope of the line

The slope of a line is the ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

Let us consider the graph given below.

In the graph given above, for every 3 units of change on x-axis, there is a change of 2 units on y-axis.

So, the slope of the line is

= Rise / Run

= 2/3

Let (x₁, y₁) and (x₂, y₂) be the two points on the a line.

Then, the formula to find the slope of a straight line is

**Example 1 : **

Find m the slope of the line.

**Solution : **

**Step 1 :**

Choose two points on the line.

P₁(x₁, y₁) P₂(x₂, y₂)

**Step 2 :**

Find the change in y-values (rise = y₂ - y₁) and the change in x-values (run = x₂ - x₁) as you move from one point to the other.

rise = y₂ - y₁ run = x₂ - x₁

rise = 4 - 2 run = -6 - (-3)

rise = 4 - 2 run = -6 +3

rise = 2 run = -3

**Step 3 :**

m = rise / run

m = (y₂ - y₁) / (x₂ - x₁)

m = 2 / (-3)

m = -2/3

**Example 2 : **

The graph shows the rate at which water is leaking from a tank. The slope of the line gives the leaking rate in gallons per minute. Find the slope of the line.

**Solution :**

**Step 1 :**

Choose two points on the line.

P(x₁, y₁) = P(4, 3)

Q(x₂, y₂) = Q(8, 6)

**Step 2 :**

Find the change in y-values (rise = y₂ - y₁) and the change in x-values (run = x₂ - x₁) as you move from one point to the other.

rise = y₂ - y₁ run = x₂ - x₁

rise = 3 - 6 run = 4 - 8

rise = -3 run = -4

**Step 3 :**

m = rise / run

m = (y₂ - y₁) / (x₂ - x₁)

m = (-3) / (-4)

m = 3/4

After having gone through the stuff given above, we hope that the students would have understood how to calculate slope m".

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