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 = 14x - 3
The x-term's coefficient is 14, so the slope of the line is 14. 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.