**Find the slope from an equation :**

Usually we follow two methods to find the slope of the straight line.

(i) By comparing the given equation with the slope intercept form (y = mx + b)

(ii) Using the formula (m) = -Coefficient of x/Coefficient of y

We can use the second method, if the given equation is in the form of ax + by + c = 0

**Example 1 :**

Find the slope of the line whose equation is

x - y + 1 = 0

**Solution : **

**Method 1 :**

To find the slope of a line, we have to compare the given equation with y = mx + c.

Here m stands for slope and c stands for y-intercept.

x - y + 1 = 0

Add y on both sides, we get

x - y + y + 1 = 0 + y

x + 1 = y

y = x + 1

By comparing the given equation with general equation, we get slope (m) = 1.

**Method 2 :**

Slope (m) = -coefficient of x/coefficient of y

m = -1/(-1)

m = 1

In both ways, we will be getting the same answer

**Example 2 :**

Find the slope of the line whose equation is

5x - 3y = 0

**Solution :**

**Method 1 :**

If we want to use the first method, we have to convert the given equation in the form y = mx + c.

3y = 5x

y = (5/3)x

Slope m = 5/3

**Method 2 :**

Slope (m) = -coefficient of x/coefficient of y

m = -5/(-3)

m = 5/3

In both ways, we will be getting the same answer

**Example 3 :**

Find the slope of the line whose equation is

4x - 2y + 1 = 0

**Solution :**

**Method 1 :**

If we want to use the first method, we have to convert the given equation in the form y = mx + c.

2y = 4x + 1

y = (4/2)x + (1/2)

y = 2 x + (1/2)

Slope m = 2

**Method 2 :**

Slope (m) = -coefficient of x/coefficient of y

m = -4/(-2)

m = 2

In both ways, we will be getting the same answer

**Example 4 :**

Find the slope of the line whose equation is

10x + 15y + 6= 0

**Solution :**

**Method 1 :**

If we want to use the first method, we have to convert the given equation in the form y = mx + c.

15y = -10x - 6

y = (-10/15)x - (6/15)

y = (-2/3) x - (2/5)

Slope m = -2/3

**Method 2 :**

Slope (m) = -coefficient of x/coefficient of y

m = -10/15

m = -2/3

In both ways, we will be getting the same answer

**Example 5 :**

Find the slope of the line whose equation is

5x + 3y - 15 = 0

**Solution :**

By using the second method, we can easily find the slope of the given line.

m = - coefficient of x/coefficient of y

= -5/(-3)

= 5/3

Hence, the slope of the given line is 5/3.

**Example 6 :**

Find the slope of the line whose equation is

2x - y + 16 = 0

**Solution :**

By using the second method, we can easily find the slope of the given line.

m = - coefficient of x/coefficient of y

= -2/(-1)

= 2

Hence, the slope of the given line is 2.

After having gone through the stuff given above, we hope that the students would have understood "Find the slope from an equation".

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