Slope-Intercept for Dummy Algebra Students

graph of y = 2x - 7

It's time, we guess, to harp on the notion of "internet stupidification" again. It's bad enough that the internet is full of bullshit claims and fake statements, but when one of the more egregious offenders among websites actually removes valid information and replaces it with bogosity, we end up with the faint taste of barf in our collective mouth. That, however, is precisely what Leaf Group did with the Sciencing.com post "How to Find B in Y=MX + B [sic]"¹; rewritten by one Kevin Beck.

Let's get the answer out of the way right up front. We'll assume that some poor schmuck wants to pull the value of the y-intercept out of a linear equation (Ax + By + C = 0). Here's an example using the equation 4x + 2y - 6 = 0

1. Move the three terms into the standard form (subtract 4x from and add 6 to both sides of the equation):  2y = -4x + 6
2. Reduce the y coefficient to 1 (divide everything by 2): y = -2x + 3
3. There you have it: the b term is 3

Strangely enough, the person whose post Beck's version replaced is five-time DotD Chance E. Gartneer, himself often a stranger to any mathematics more advanced than counting on his fingers and, perhaps, toes. In this case, however, Gartneer's post was nominally correct for once. Overblown and wordy, to be sure, but correct.

Beck, on the other hand, made some mistakes...

He started with some problems in notation:

"...b is the y-intercept, or the point (0. y) at which the the line crosses the y... axis."

Umm, no, Kev and CE: the point is (0,y): that's supposed to be a comma, not a period. Messing up your punctuation in a mathematical discussion is... inadvisable. That's not, however, Beck's most serious flub. No, that comes next:

"If you already have an equation in this form, finding b is trivial. For example, in: y = -5x -7, All [sic] terms are in the proper place and form, because y has a coefficient of 1. The slope b in this instance is simply -7."

Well no,  Kevin, the slope is (-5) and the y-intercept is (-7). Proofread much? Kevin then proceeds to attempt the solution of the equation 6x - 3y = 21, in which he comes to the conclusion that,

"The y-intercept b is therefore -7."

Our staff mathematician was gratified to note that Beck's answer was correct, On the other hand, she was flabbergasted to note that Kevin somehow managed to come to this answer from the equation y = -2x - 7... which, unfortunately, he says results in a slope of -2... but the slope is actually positive 2. In rearranging the terms from the equation 2x - y = 7, he subtracted 2x from both sides and ended up with -y = 2x + 7. Except the answer is actually -y = -2x + 7 which, when set in the standard format, is y = 2x - 7. Oops. Looks like our Dumbass of the Day forgot all the elementary math he took while editing magazines...

¹ Yes, we know that in the standard form of a linear equation (y = mx + b), the coefficients are lower-case letters, but hey: it's eHow...

copyright © 2018-2023 scmrak

MM - ALGEBRA