Finding the Intercept for Dummies

Slope-intercept form of linear equation

One of our staffers here at the Antisocial Network minored in math and computer science while getting a science degree. That doesn't mean he's a math whiz, it just means that he didn't have enough courses in any other subject to declare a minor. He's fairly good at algebra and geometry, though, and given enough time he can remember how to use trigonometry. Whatever... He once observed that people who understand math usually aren't good at teaching it. For proof, read any calculus textbook published before about 1990 and look for the phrase "it's intuitive." It's not! That doesn't mean that people who aren't good at math are good at teaching it, though: take a look at the mess eHow.com's Gwendolen Akard made of trying to explain "How to Find the Y Intercept."¹

Although a self-appointed specialist in fitness and music who "wrote professionally for her high school newspaper" (she got paid by a high-school newspaper? no one around here ever did!), Gwen retains only a tenuous grasp on mathematics. We say that because, though she managed to more or less correctly -- although awkwardly, we feel -- define the Y-intercept of a line:

"The y-intercept is an integral concept when working with graphs in mathematics. It is, most simply, the point where a line crosses the y-axis. You can find its value most simply by looking at the graph. However, you can also find its value without a picture, but by using an algebraic equation that represents the graph itself"...

...she apparently doesn't know the difference between a line and a graph: in other words, graphs don't have "algebraic equations," lines do. But what would we simpletons know? Akard proceeds to next tell her readers how to find the Y-intercept by looking at a graph of the equation -- yes, she took four friggin' steps to tell you how to read the Y-intercept off a graph, but not how to draw the graph in the first place -- for that you need, duh, the Y-intercept.

Next, Gwen goes through a torturous set of five steps for finding the intercept from the line's equation. She chooses as her example the equation 3x - 4y = 12. Our math guy says that calculating the intercept should only take two steps: Place the equation in the slope-intercept form ( y = mx + b):      -4y = -3x + 12 Solve the equation for y:     y = ¾x - 3  And there you have it: an intercept of -3 (not to mention a slope of 0.75). According to Akard, however, it takes four steps (her fifth step is, most simply, recording the value). Gwen's steps are

1. Write down the equation that represents the graph.
2. Set x equal to 0... The equation is now 3(0) - 4y = 12.
3. Solve for y. Multiply 3 and 0. Now you have 0 - 4y = 12, or -4y = 12.
4. Divide by the coefficient -- in this case -4 -- to get the y value alone. The equation becomes y = 12 / -4 or y = -3.

Duh: what's this whole "set x equal to 0" bullpuckey, anyway, and who says "multiply 3 and 0"? Not to mention that, if you are finding the intercept of the line, you are extremely likely to need the slope as well; and Akard not only doesn't solve for the slope of the line, she doesn't even mention it!

No, if the people to whom mathematics "is intuitive" make the worst math teachers, then our Dumbass of the Day must be a hell of a good math teacher, because she most simply has no idea what she is talking about here!

¹ The original has been deleted by Leaf Group, but can still be accessed using the Wayback machine at archive.org. The URL was   ehow.com/how_8043674_yintercept.html

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