Graphing an Equation

Date: 4/4/96 at 22:10:44
From: Anonymous
Subject: Graphing

How do you graph 2x-y = 10? I just don't understand how to do it. 
Would you please help? Thank you!

Date: 9/1/96 at 18:29:31
From: Doctor Jim
Subject: Re: Graphing

Since neither x or y has an exponent you can see, they are both called 
linear, so this equation forms a line.  

The easiest way to graph this is to pick some points (x,y) that make 
the equation true, like x=6, y=2, because 2*6-2 = 12-2=10. 
If x=7 then y=4.  In fact there are an infinite number of solutions 
for this equation.  No matter what you pick for x, you can find a 
y that will make the left side be 10.  

Another way to graph it would be to solve it for y.  
Subtract 2x from both sides so -y=-2x+10, then divide both sides 
by -1, so that y = 2x - 10.  

In this form the number in front of x is the slope. In this case the 
line goes up 2 for every 1 it goes to the right, and the y-axis 
intercept is -10, so it crosses the y-axis at (0,-10).  Remember that 
the slope means the y coordinate increases 2 every time the x 
coordinate increases 1.  So more points on the line could be found by 
adding 1 to the x and 2 to the y, i.e., (1,-8), (2,-6), (3,-4), etc.

-Doctor Jim,  The Math Forum
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