FIND THE SLOPE AND Y INTERCEPT

To find the slope and y-intercept of a line, you have to write the equation of the line in the form, 

y  =  mx + b

Here 'm' stands for slope of the line and 'c' stands for y-intercept.

Example 1 :

Find the slope and y-intercept of the line :

2x + 3y  =  7

Solution :

Write the given equation in the form y = mx + b.

2x + 3y  =  7

Subtract 2x from each side. 

3y  =  -2x + 7

Divide each side by 3.

y  =  (-2x + 7) / 3

y  =  -2x/3 + 7/3

The above equation is in the form y = mx + b. 

Then, 

slope (m)  =  -2/3

y-intercept (b)  =  7/3

Example 2 :

Find the slope and y-intercept of the line :

4x - 2y + 1  =  0 

Solution :

Write the given equation in the form y = mx + b.

4x - 2y + 1  =  0

Add 2y to each side. 

4x + 1  =  2y

Divide each side by 2.

(4x + 1) / 2  =  y

4x/2 + 1/2  =  y

2x + 1/2  =  y

(or)  y  =  2x + 1/2 

The above equation is in the form y = mx + b. 

Then, 

slope (m)  =  2

y-intercept (b)  =  1/2

Example 3 :

Find the slope and y-intercept of the line : 

3x - 9y + 3  =  0 

Solution :

Write the given equation in the form y = mx + b.

3x - 9y + 3  =  0

Add 9y to each side. 

3x + 3  =  9Y

Divide each side by 9.

(3x + 3) / 9  =  y

3x/9 + 3/9  =  y

x/3 + 1/3  =  y

(or)  y  =  x/3 + 1/3 

The above equation is in the form y = mx + b. 

Then, 

slope (m)  =  1/3

y-intercept (b)  =  1/3

Example 4 :

Find the slope and y-intercept of the line : 

5x + 7y + 1  =  0 

Solution :

Write the given equation in the form y = mx + b.

5x + 7y + 1  =  0 

Subtract 5x and 1 from each side.

7y  =  -5x - 1

Divide each side by 7.

y  =  (-5x - 1) / 7

y  =  -5x/7 - 1/7

The above equation is in the form y = mx + b. 

Then, 

So, 

slope (m)  =  -5/7

y-intercept (b)  =  -1/7

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