# Change between Slope-Intercept and Standard Form

In a finite mathematics course, you may be asked to solve algebra problems using different forms of the same linear equation—for example, slope-intercept versus standard.

You can change from one form of a linear equation to another by using basic algebra. The choice of the form of the line—whether slope-intercept or standard—just depends on the particular process being performed.

## Changing to slope-intercept form

To change the equation 4*x* – 5*y* = 20 to the slope-intercept form, you first isolate the y-term on the left side. To do that, subtract 4*x* from each side, and you get –5*y* = –4*x* + 20. Then divide each term by –5; the final equation is

You can immediately tell that the slope is 4/5 and the y-intercept is at –4; the coordinates of the *y*-intercept are (0, –4).

## Changing to the standard form

In order to change the equation

to the standard form, the first thing to do is to multiply each term by 8. This gives you 8*y* = –3*x* + 56. To put it in standard form, you add 3*x* to each side; the standard form is 3*x* + 8*y* = 56. The slope of –3/8 and *y*-intercept of 7 were more obvious in the original form, but you can pick up the x-intercept by using C/A; the *x*-intercept is at the point