Slope-Intercept for Dummies

graph of y = -2/3x + 3

It can be just a little amusing – infuriating, too – to see the kind of mess made of even the most elementary mathematics posts by people who studiously avoided any form of mathematics while in college. Watching a J-school grad tackle complex geometry problems, for instance, is an exercise in utter confusion. Apparently, some B-school¹ grads have it just as bad; grads like Bradley James Bryant, who demonstrated critical innumeracy in "How to find Y Value for the Slope of a Line" at Sciencing.com.

You need to know two things up front: first, the topic makes no sense. Second, "Bradley James" uses female pronouns. But back to the first: it makes no sense because slope is a number and not a coordinate (x,y) pair. We suspect that the OQ wanted to know how to find the Y-intercept of a line given the slope and/or formula, but no one will ever know...

Bryant, forced to pound out 300 words or so to answer a query that could have been covered in a third of that verbiage, opened by attempting to explain graphs. That's where Bradley James first went off the tracks, a divergence that began with the sentence,

"One of the most important relationships of the xy [sic] graph is the line called the 'slope' or angle of the line from the center point."

We truly hate to disabuse Bryant of this notion, but we simply MUST point out that only a tiny fraction of possible lines on the Cartesian plane pass through the origin. The slope is independent of a line's location on the graph!

Once she had that out of the way, Bradley James went on to attempt to explain how one might find the y coordinate. In her math, you can find Y...

"...if you know the slope of the line and the x coordinate."

Nope, you can't: you need to know the slope and the intercept. Bryant explained to us that the slope of a line equals [y1 - y2] / [x1 - x2], which is true. However, Bradley James then jumped from that revelation to,

"Graph a line with the following equation: y = -(2/3)x + 3."

Wait, what? Now we know both the slope (⅔) and the y-intercept (3). Of course you can solve an equation for y if you know x, but that isn't what the OQ asked: the OQ wanted to know how to find Y from the slope (which is impossible, but Bryant never mentioned that). Not only that, but Bradley James also managed to botch her example:

"Graph a line with the following equation: y = -(2/3)x + 3... If x = 3, then y = -2 (( 2/3 )(3) – 4 = 2 – 4)."

No, you blithering idiot, y = 1! 

And the content editor let this crap pass, and Demand Media paid our Dumbass of the Day to get the whole thing wrong!  Sheesh!

¹ Business school instead of journalism (J-school)...

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