### 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 6*y* + 4*x* = 7 to slope-intercept form.

6*y* + 4*x* = 7

6*y* = - 4*x* + 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 3*x* = 4*y* + 8 to point-slope form.

3*x* = 4*y* + 8

3*x* - 8 = 4*y*

*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(- )

-5*x* + 4*y* = - 14*general linear form*