Change between Slope-Intercept and Standard Form

By Mary Jane Sterling

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 4x – 5y = 20 to the slope-intercept form, you first isolate the y-term on the left side. To do that, subtract 4x from each side, and you get –5y = –4x + 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 8y = –3x + 56. To put it in standard form, you add 3x to each side; the standard form is 3x + 8y = 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