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

Answer 1

Different people have different methods that they like to use, but there's one step

that's absolutely indispensible that everybody positively has to do:

Before you can find the slope-intercept form of an equation, it's absolutely essential

that you have to know what the slope-intercept form looks like, so that when you

see 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 itself

on 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 from

all 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, because

whatever you do to the side where 'y' is, you must do exactly the same thing

to 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 -14

Isn't that thje ugliest mess you ever saw ! How in the world can we get 'y' all alone

on one side ?

If you just do one little step at a time, it's not hard at all. Just remember: Whatever you do

on 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 that

doesn't help the dishes get washed. It just makes the job a little bit longer, but

it doesn't hurt anything.

OK. Enough. Let's wipe out this equation. I'm picking the steps, because I want to

get 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 -14

and then immediately, before you forget, add 11x to the right side:

2y = 12x -14

That looks better already! Look at it for a second. What do you have to do to the left side now

to 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 - 14

Now quickly, before you forget, divide the right side by 2 also:

y = 6x - 7

Believe it or not, that's it! That's the form you want. The reason why the form

matters is that now, in that form, you can look at the equation and tell somebody

exactly 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 equation

is called the 'slope-intercept' form.