CONVERTING GENERAL FORM TO SLOPE INTERCEPT FORM

In this section, you will learn how to convert a linear equation in general form to slope-intercept form.

General form

Slope-intercept form

ax + by + c = 0

y = mx + b

Example 1 :

Write the following general form equation of a line in slope-intercept form : 

3x - y + 1  =  0

Solution :

3x - y + 1  =  0

Add y to each side. 

3x + 1  =  y

or

y  =  3x + 1

Example 2 :

Write the following general form equation of a line in slope-intercept form : 

x - 2y + 6  =  0

Solution :

x - 2y + 6  =  0

Add 2y to each side. 

x + 6  =  2y

Divide each side by 2.

(x + 6)/2  =  y

x/2 + 6/2  =  y

x/2 + 3  =  y

or

y  =  x/2 + 3

Example 3 :

Write the following general form equation of a line in slope-intercept form : 

14x + 4y - 1  =  0

Solution :

14x + 4y - 1  =  0

Subtract 14x from each side.

4y - 1  =  -14x

Add 1 to each side. 

4y  =  -14x + 1

Divide each side by 4.

y  =  (-14x + 1)/4

y  =  -14x/4 + 1/4

y  =  -7x/2 + 1/4

Example 4 :

Write the following general form equation of a line in slope-intercept form : 

15x + 12y + 2  =  0

Solution :

15x + 12y + 2  =  0

Subtract 15x and 2 from each side. 

12y  =  -15x - 2

Divide each side by 12. 

y  =  (-15x - 2)/12

y  =  -15x/12 - 2/12

y  =  -5x/4 - 1/6

Example 5 :

Write the following general form equation of a line in slope-intercept form and graph the line.  

2x - y + 1  =  0

Solution :

2x - y + 1  =  0

Add y to each side . 

2x + 1  =  y

(or)  y  =  2x + 1

The equation 'y  =  2x + 1' is in the form of 

y  =  mx + b

Then, 

m  =  2

b  =  1

Because slope '2' is a positive value, the line will be a rising line.

And also,

rise/run  =  2

rise/run  =  2/1

Then,

rise  =  2

run  =  1

Because the y-intercept is 1, the line will intersect y-axis at 1. 

Graphing : 

Step 1 :

Plot the y-intercept at (0, 1). 

Step 2 :

Because the run is 1, move 1 unit to the right from (0, 1).

Step 3 :

Because the rise is 2 and the line is rising line, move 2 units up from the position reached in step 2.   

Now, you are at (1, 3). 

Connect the points (0, 1) and (1, 3) to get the line.  

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