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/

## Friday, 21 August 2009

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