Quote:
Originally Posted by Tinaa
I'm tutoring a friend in college algebra. She probably one of the most anal people (structured) I know, yet she cannot get basic college algebra. I've explained that one must follow the rules. She is learning graphing...basic Y= mx+b. She doesn't understand that b = y - intercept. Why doesn't y = y - intercept? m = slope but why doesn't x = x intercept? Arrrgh! HELP!
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From the questions you write, I would say that you need to insist on a couple of ideas with her:
- In analytic geometry, equations such as y=mx+b are a shorthand way of describing curves.
- The letters m and b are constants, but the letters x and y stand for arbitrary numbers. Make sure she grasps the difference between a symbolic constant and a variable, which can be subtle at first. Constants represent fixed values which we may not care to specify. Variables represent all possible values in a certain range. Context matters here, alas.
- We interpret each particular pair (x, y) as the coordinates of a point in a cartesian system (if she is completely new to this, reminding her of the battleship game might be helpful here). The equation y=mx+b is supposed to represent all the points in the line at once. It's a "test" we do to check whether some point in the plane belongs to the line or not. Particular pairs (x, y) which verify the equality y=mx+b fall along the line; points which do not verify the equality fall outside it. (A more suggestive notation might be (x0, y0); in any case, try to get her used to both notations, and to switching between equivalent notations.)
On a final note, I was not familiar with the term "
y-intercept". I've only ever heard "intercept". Is it standard in English?