# 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. Kindly mail your feedback to v4formath@gmail.com

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