# Algebra: Slope-Intercept Form

## Slope-Intercept Form

Are you wondering why I asked you to solve the linear equations in the above exercises for *y*? I wasn't just making you jump through hoops (although I am impressed by your agility, I must admit); there's actually a very good reason to do it. Once a linear equation is solved for *y*, it is said to be in *slope-intercept form*.

There are two big benefits that result when you put an equation in slope-intercept form (and you can probably figure out what they are based on the name): You can identify the slope and *y*-intercept of the line (get this) *without doing any additional work at all*! Plus, if you transform equations while you do sit-ups, the slope-intercept form could actually give you greater definition in your abs!

Let's get mathematical for a moment. Officially speaking, the slope-intercept form of a line is written like this:

*y*=*mx*+*b*, where*m*is the slope and*b*is the*y*-intercept

##### Talk the Talk

Once a linear equation is solved for *y*, it is in **slope-intercept form**, *y* = *mx + b*. The coefficient of the *x* term, *m*, is the slope of the line and the number (or **constant**), *b*, is the *y*-intercept.

In other words, once you solve a linear equation for *y*, the coefficient of *x* will be the slope of the line, and the number with no variable attached (called the *constant*) marks the spot on the *y*-axis, (0,*b*), where the line passes through.

##### You've Got Problems

Problem 2: Identify the slope and the coordinates for the *y*-intercept given the linear equation 3*x* + 2*y* = 4.

**Example 2**: Identify the slope and the coordinates for the *y*-intercept given the linear equation *x* - 4*y* = 12.

**Solution**: Remember, all you have to do to transform an equation into slope-intercept form is to solve it for *y*. To isolate the *y*, subtract *x* from both sides of the equation and then divide everything by the coefficient of - 4:

- -4
*y*= -*x*+ 12 *y*=^{1}⁄_{4}*x*- 3

The *x*-term's coefficient is ^{1}⁄_{4}, so the slope of the line is ^{1}⁄_{4}. Since the constant is -3, the graph of the equation will pass through the *y*-axis at the point (0,-3). (Don't forget that the *x*-coordinate of a point on the *y*-axis will always be 0, and vice versa.)

Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with **Alpha Books**, a member of Penguin Group (USA) Inc.

You can purchase this book at Amazon.com and Barnes & Noble.