why is the y intercept called b
The various "standard" forms are often holdovers from a few centuries ago, when mathematicians couldn't handle very complicated equations, so they tended to obsess about the simple cases. Nowadays, you likely needn't worry too much about the "standard" forms; this lesson will only cover the more-helpful forms. y = mx + b m " is the b y -. (For a review of how this equation is used for graphing, look at. )
I like slope-intercept form the best. It is in the form " y ", which makes it easiest to plug into, either for graphing or doing word problems. Just plug in your x -value; the equation is y. Also, this is the only format you can plug into your (nowadays obligatory) graphing calculator; you have to have a " y " format to use a graphing utility.
But the best part about the slope-intercept form is that you can read off the slope and the intercept right from the equation. This is great for, and can be quite useful for. Common exercises will give you some pieces of information about a line, and you will have to come up with the equation of the line. How do you do that? You plug in whatever they give you, and solve for whatever you need, like this: m ( 1, 6). What if they don't give you the slope? ( 2, 4) (1, 2).
As you can see, once you have the slope, it doesn't matter which point you use in order to find the line equation. The answer will work out the same either way. Reading really old maths, even when it's been translated well into modern English, can be very tedious. It makes it hard to follow even fairly simple derivations, in my limited experience. But it is a rewarding experience to try get into the heads of the mathematicians of other times cultures. In ancient times, geometry had an edge over algebra. It was assumed that Euclidean geometry was truly the geometry of the world. So geometric proofs were seen as far more tangible than the abstract word jugglery of algebra.
Even by the time of Newton that attitude prevailed, so all the proofs in his are given in geometric form, to make them more plausible to his audience. Early algebra was very geometric in character. They wouldn't form expressions like ax + b, because it's not logical to add an area to a length. They'd have to express it as the sum of two areas. The programmer in me wants to use uppercase for constants and lowercase for variables. But sometimes I use that distinction to distinguish matrices, vectors or other sets from their elements.
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