How do you find a slope-intercept form of an equation? - Answers

Different people have different methods that they like to use, but there's one stepthat's absolutely indispensible that everybody positively has to do:Before you can find the slope-intercept form of an equation, it's absolutely essentialthat you have to know what the slope-intercept form looks like, so that when yousee it, you'll grab it, and you won't just ignore it and keep looking for it.The slope-intercept form of the equation is the form where you have 'y' all by itselfon one side, and everything else ... the 'x' and all the numbers ... on the other side.So here's how you find that form:-- Take the equation that you're given in class, in the book, or in the homework.-- Sit still and look at it. Look at all its parts. Look at what's on each side of the 'equals' sign.Look to see if there's any number stuck to 'y'. Then start working.-- One step at a time, do whatever you have to, to get 'y' separated out fromall the other stuff on the same side with it, and get 'y' all alone on one side.-- Most important: Keep track of exactly what you do in each step, becausewhatever you do to the side where 'y' is, you must do exactly the same thingto the other side of the equation.Now we'll do an example. Well, actually, I'll do it, and you'll watch.-11x + 2y = x -14Isn't that thje ugliest mess you ever saw ! How in the world can we get 'y' all aloneon one side ?If you just do one little step at a time, it's not hard at all. Just remember: Whatever you doon one side of the equation, you must do exactly the same thing on the other side.How do you know what step to do ? What if you do the wrong step ? :-(No problem! Doing the wrong step doesn't hurt anything. It just doesn't help.It's like if you have to wash the dishes, then painting your toenails is a step thatdoesn't help the dishes get washed. It just makes the job a little bit longer, butit doesn't hurt anything.OK. Enough. Let's wipe out this equation. I'm picking the steps, because I want toget this answer done and go get a snack, but this is notthe only right way to do it:Add 11x to the left side:2y = x -14and then immediately, before you forget, add 11x to the right side:2y = 12x -14That looks better already! Look at it for a second. What do you have to do to the left side nowto get 'y' all alone there ? You have 2y there right now. That's double what you want.To make it just one 'y', you have to take 1/2 of what's there. Another way to say "take half"is "divide by 2".Divide the left side by 2:y = 12x - 14Now quickly, before you forget, divide the right side by 2 also:y = 6x - 7Believe it or not, that's it! That's the form you want. The reason why the formmatters is that now, in that form, you can look at the equation and tell somebodyexactly what the line will look like if he draws the graph of that equation.The slope of the line is ' 6 ', and the intercept is ' -7 '. And that's why this form of the equationis called the 'slope-intercept' form.