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### Formulas for the Equation of a Line

```
Date: 09/28/98 at 23:25:57
From: Michelle
Subject: Algebra II: point slope formula

My question isn't about how to use point slope formula, but more of
what it is used for. Given a problem, I can accurately use:

y - y1 = m(x - x1)

to get the answer, but I don't understand what its specific meaning
is. Is it just another way of getting to a y = mx + b style formula
suitable for graphing, or does it serve some other purpose?

Thank you,
Michelle
```

```
Date: 09/29/98 at 12:56:20
From: Doctor Peterson
Subject: Re: Algebra II: point slope formula

Hi, Michelle. Good question! Too often people learn formulas but don't
stop to ask what they are for.

There are several different ways to write the equation of a line, and
each is designed to be used when you have certain pieces of information
to start with. You could do everything with one form, such as slope-
intercept, but often it's easier to use a form specially designed for
one case. For example, there are:

Slope-intercept:    y = mx + b

Slope-x-intercept:  y = m(x - a)

Point-slope:        y - y1 = m(x - x1)

Two-point:          y - y1   y2 - y1
------ = -------
x - x1   x2 - x1

Two-intercept:       x     y
--- + --- = 1
a     b

These are all equivalent, and which one you use just depends on what
you are given. But you don't have to memorize all of them. If you
understand how graphs work, you can figure everything out when you need
to. All these forms (except for the two-intercept form) are just ways
of saying that the slope is constant. Either you are given the slope
(m), or you figure out the slope (y2 - y1) / (x2 - x1), and then you
compare the general point (x, y) with either an intecept (0, b) or
(a, 0), or a general point (x1, y1).

So the "meaning" of the point-slope form is simply that you can get the
rise (y - y1) by multiplying the run (x - x1) by the given slope. You
can graph it as it stands (by identifying the point and the slope), or
you can change it into any other form you want. It's yours to use any
way you like.

I hope that helps!

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Linear Equations
Middle School Algebra
Middle School Equations

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