Algebra: 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 3x + 2y = 4.
Example 2: Identify the slope and the coordinates for the y-intercept given the linear equation x - 4y = 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:
- -4y = -x + 12
- y = 1⁄4x - 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.