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Graphing y = mx + b


Date: 01/20/97 at 10:58:13
From: Larry Shirley
Subject: x and y intercepts and graph

Dear Dr. Math,

I am having trouble understanding 3x + 2y = 5.  This has to be in 
y = mx + b form.  After I get it in the proper form, how do I graph 
it?

Sarah


Date: 01/20/97 at 11:59:07
From: Doctor Lisa
Subject: Re: x and y intercepts and graph

Hi Sarah!

Let's take a look at your question step by step.  The first thing you 
told me is that you need to get the equation into y = mx + b form.  
So, to begin, you will work on solving this equation for y.  As you 
may recall, what that means is that you want to manipulate the 
equation so you get y by itself on one side of the equation.  This is 
the process I would use:

3x + 2y = 5
     2y = -3x + 5     (subtract 3x from each side to get 2y by itself)
      y = -3/2x + 5/2 (divide both sides by 2 to get y by itself)

Now that I have the equation in the proper form, we're ready to 
graph it.

Remember that y = mx + b is called "slope-intercept form."  If you 
have an equation in this form (and written with the x-term first and 
the constant second), you will have the slope and the y-intercept for 
the graph.  The slope is "m" (the coefficient of x) and is the rise 
over the run (or the change in y over the change in x).  The 
y-intercept is "b" and is where the graph crosses the y-axis.

In this problem, m = -3/2 and b = 5/2.  I would first locate the 
y-intercept on the graph.  Since b = 5/2, I would find where 5/2 (or 
2 1/2) is on the y-axis and make a point.  This is where the graph 
crosses the y-axis.  

From there, I would use the slope to find other points on the graph.  
When using slope, we first travel in the y direction and then move in 
the x direction.  Keep in mind that a positive y direction is up, a 
negative y direction is down, a positive x direction is right, and a 
negative x direction is left.  When you have a positive slope, you 
will either use a positive y and positive x movement or a negative y 
and negative x direction. This is because a positive number divided by 
a positive number is still positive and a negative number divided by a 
negative number is also positive.  Since we have a negative slope, we 
need one positive number and one negative number.  

**  As I am describing the graphing process below, I am assuming 
that you are using graph paper.  This process will work with any scale 
on the graph (1 square could equal 2 units or 10 units, etc.).  **

Our slope is -3/2.  This means I can do one of two things: either go 
up 3 squares (positive direction) and left 2 squares (negative 
direction) or go down 3 squares (negative direction) and right 2 
squares (positive direction).  Be careful with this problem because 
you are beginning with a fraction (the 5/2 from above) - you'll have 
to either estimate where halfway is or make each mark equal to 1/2 (in 
other words, 2 marks on the graph = 1 unit). 

Go to the 5/2 you marked earlier.  You can go up 3 squares from the 
5/2 and then move over left 2 squares and make your next point.  You 
can also go down 3 squares from the 5/2 and then move over right 2 
squares and make your next point.  If you do both of those operations, 
you will have 3 points and can connect the dots to make a line.  You 
can count out as many points as you need to make the line, but I 
suggest a minimum of 3 points for accuracy (although some teachers 
want you to use 5 points).  The more points you have, the more 
accurate the line will appear on your graph.  

I hope I clearly answered your question for you and that this will 
help you do other problems similar to it.  Have a great day!

-Doctor Lisa,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Graphing Equations

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