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Sketch an Equation


Date: 10/07/97 at 15:40:59
From: April
Subject: Algebra

I have this algebra problem:

   -3x+2y = -6       

I need to sketch it using the slope and y-intercept. Before I do that, 
how do I rearrange the problem so I can sketch it?

Thank you.


Date: 10/10/97 at 11:49:46
From: Doctor Chita
Subject: Re: Algebra

Hi April:

Linear equations with two variables, such as the one you've asked 
about, can be written in a number of ways. The way you write a linear 
equation depends on the information you want. Here are three types:

(1) general form ax + by = c 
    This is like the equation you've asked about.

(2) slope-intercept y = mx + b 
    This is the form you want. An equation in this form is easy to 
    graph because you have the slope, m, and the y-intercept, b.

(3) point-slope  (y-y1) = m(x-x1) 
    The slope is m and the point is (x1,y1). This is a variation of  
    the slope-intercept form. Instead of having (0, b) the intercept,  
    you have a specific point not on the y-axis. It's an easy form to 
    use because you can plot the point and use the slope of the line 
    to draw the line through that point.

So, to get from the general form to the slope intercept form, you need 
to isolate the y-term on one side of the equation. If we start with 
the general form:

 ax + by = c

Subtract the ax term from both sides:

      by = c - ax

Rewrite the right side, putting the x-terms first (this isn't 
necessary, but it looks better):

      by = -ax + c

Divide both sides by b:

    by/b = -ax/b + c/b

       y = -ax/b + c/b

The slope is -a/b and the y-intercept is c/b.

Use this procedure to rewrite your equation and you should be all set.
 
-Doctor Chita,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra
Middle School Algebra

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