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### Graphing Equations

Date: 08/15/97 at 05:06:34
From: Elizabeth
Subject: Name of a graphing equation

I need to find out how to graph the following equations. I know the
coordinates but would like to know the name and where I can graph
them.

They are as follows:  4x-2y = 5
x = 3y-1

and:      y = 2x+7
y = -x-3

Your help would be greatly appreciated!
Elizabeth

Date: 08/15/97 at 08:19:44
From: Doctor Jerry
Subject: Re: Name of a graphing equation

Hi Elizabeth,

All of these are equations of a line.  They all can be put into the
form

A*x+B*y = C.

The last two equations have the form y=m*x+b. These are often called
the point-slope form of a line. The number m is the slope of the line
and b is the y-intercept.

To graph any one of these equations, all you need is two points that
satisfy them. Since a line is completely determined by two of its
points, this is all you need.

The equation 4x-2y = 5, for example, is an equation for a line that
goes through the points (0,-5/2) and (5/4,0). To find these two
points, I first let x = 0 in the equation: 4*0-2y = 5. This is the
same as -2y = 5 or y = -5/2, so (0,-5/2) is a point on the line.
Next, let y = 0 in the equation and solve for x. This gives (5/4,0).

You can do the same with y=2x+7: (0,7) and (-7/2,0) are two points on
the line. Or you can notice that the slope of the line is 2 and its
y-intercept is 7. If you know about slope, you can plot the line with
this information.

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

Associated Topics:
High School Equations, Graphs, Translations

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