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

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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

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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

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