# Writing Equations

### Converting Among Forms

#### Converting Among Forms

The goal in converting an equation to slope-intercept form is to isolate y on one side of the equation. Thus, to convert to slope-intercept form, perform inverse operations on variable terms and constant terms until y stands alone on one side.

Example: Convert 6y + 4x = 7 to slope-intercept form.

6y + 4x = 7
6y = - 4x + 7
y = - x +
y = - x + slope-intercept form

Slope-intercept form can be thought of as a specific case of point-slope form, in which the "point" is the y -intercept. Thus, to convert to point-slope form, first convert to slope-intercept form, then move the constant term b to the left side of the equation (or isolate x and then divide by the y coefficient).

Example: Convert 3x = 4y + 8 to point-slope form.

3x = 4y + 8
3x - 8 = 4y
x - = y
x - 2 = y
y = x - 2 slope-intercept form
y + 2 = x point-slope form

The goal in converting an equation to general linear form is to place x and y on one side of the equation and convert all coefficients (and the constant term) to integers. Thus, to convert to general linear form, first isolate x and y on one side and the constant term on the other side. Next, if any of the coefficients are fractions, multiply the entire equation by the least common denominator of all the fractions.

Example: Convert y + 1 = (x - 2) to general linear form.

y + 1 = (x - 2)
y + 1 = x -
- x + y + 1 = -
- x + y = - - 1
- x + y = -
4(- x + y) = 4(- )
-5x + 4y = - 14 general linear form

Remember--all forms of an equation describe the same line because they have the same solution set.

## Take a Study Break

### What's your Pretty Little Liars name?

Take this quiz to find out!

### Which young actress just got married?

Click to find out!

### Cat bearding WINS THE INTERNET

Have you seen this yet?

### Scary movies with funny posters

These. Are. Hilarious.

### Geeky Actors: Then and Now

Travel back in time!

### Villains We Want These Actresses to Play

From super cute to super bad!

### 10 Movies Better Than Their Books

What do you think?