Interpreting Slopes

Date: 09/14/98 at 21:32:39
From: Lauren Poss
Subject: Algebra II

Determine whether the graph of each equations rises to the right, 
falls to the right, is horizontal, or is vertical:

   x + y = 3
   2x + 12 = 0     
   2x - y = 6   
   2x + 3y + 32 = 0    
   2x - 3y = 0    
   2y + 7 = 3.5(4)

Thank you for your time.  
Sincerely,
Lauren Poss

Date: 10/20/98 at 19:48:58
From: Doctor Whitworth
Subject: Re: Algebra II

Dear Lauren:

The equations that you are referring to are all linear equations.  
This means that they are all straight lines. Your problem involves the 
nature of the slope of the equations.

We can write an equation in the following form:

   y = mx + b

In this form, the slope can easily be determined. It is the value that 
is represented by m.

   If the slope is positive (e.g. y = 3x + 4), m is a positive number 
   and the slope rises to the right. 

   If the slope is negative (e.g. y = -3x + 4), the slope falls to the    
   right. 

   If the slope is zero (e.g. y = 7), the straight line is horizontal. 

   If there is no slope (e.g. x = 3), the straight line is vertical.

To solve your problems, you should solve each equation for y, if 
possible, and find out whether your m value is positive, negative, 
zero, or not present.

For example, we'll work on your third problem: 2x - y = 6. To solve 
this for y, you must move the x variable to the right side of the
equation:

   -y = -2x - 6

Then divide all terms by negative one:

    y = 2x + 6

In this case, the number in front of the x is positive, so that the m 
value is positive two, which means that the straight line rises to the 
right.

In your fourth problem, you have:

   2x + 3y + 32 = 0

If you move the 2x and 32 to the right of the equal sign, you get:

   3y = -2x - 32 

Dividing both sides by 3:

    y = (-2/3)x - 32/3

Since the slope m is negative, the line falls to the right.

Best of luck to you,

- Doctor Whitworth, The Math Forum
Check out our web site! http://mathforum.org/dr.math/