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.