# CONVERTING STANDARD FORM TO SLOPE INTERCEPT FORM

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

 Standard form Slope-intercept form ax + by = c y = mx + b

Example 1 :

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

3x - y  =  -1

Solution :

3x - y  =  -1

Subtract 3x from each side.

-y  =  -3x - 1

Multiply each side -1.

y  =  3x + 1

Example 2 :

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

x - 2y  =  -6

Solution :

x - 2y  =  -6

Subtract x from each side.

-2y  =  -x - 6

Multiply each side by -1.

2y  =  x + 6

Divide each side by 2.

y  =  (x + 6)/2

y  =  x/2 + 6/2

y  =  x/2 + 3

Example 3 :

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

14x + 4y  =  1

Solution :

14x + 4y  =  1

Subtract 14x from 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 standard form equation of a line in slope-intercept form :

15x + 12y  =  -2

Solution :

15x + 12y  =  -2

Subtract 15x 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 standard form equation of a line in slope-intercept form and graph the line.

2x - y  =  -1

Solution :

2x - y  =  -1

Subtract 2x from each side.

-y  =  -2x - 1

Multiply each side by -1.

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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