Associated Topics || Dr. Math Home || Search Dr. Math

Graphing Slanted Lines

```
Date: 07/22/97 at 16:05:47
From: P. J.  Richardson
Subject: Graphing slanted lines

When graphing slanted lines what does it mean when the instructions
say add, subtract, or divide both sides by a particular number? And
how do you know when to add, subtract, or divide?  Please give an
example.

Regards, P.J.
```

```
Date: 07/28/97 at 12:22:03
From: Doctor Rob
Subject: Re: Graphing slanted lines

Suppose you had the equation 2*x - 3*y + 5 = 0. Since it has degree 1,
it is the equation of a line. As an equation, it has two sides: the
left, 2*x - 3*y + 5, and the right, 0.

You are going to try to solve this equation for y. The way to do that
is to move terms from one side to the other by adding something to
both sides. For example, to move the 5 from the left side to the
right, add -5 to both sides. Since -5 = -5, and equals added to equals
are equal, you get

(2*x - 3*y + 5) + (-5) = 0 + (-5)

or, in other words,

2*x - 3*y = -5.

Move the 2*x term to the other side by adding -2*x = -2*x to this last
equation:

2*x - 3*y + (-2*x) = -5 + (-2*x),
or

-3*y = -2*x - 5.

We have isolated y on one side of the equation, and everything else on
the other side, which is desirable. Now we are going to divide this
equation by -3 = -3. Since equals divided by nonzero equals are equal,
we will get a true equation:

(-3*y)/(-3) = (-2*x - 5)/(-3)

or

y = (2/3)*x + (5/3).

This completes the process of solving for y. We solved for y to put
the equation into the slope-intercept form, y = m*x + b.

In this form, y = m*x + b, you can read off m = 2/3 and b = 5/3.
m is the slope of the line, and b is the y-intercept, that is, the
point (0,b) on the line and also on the y-axis. Now you can graph the
line quite easily.

Another method is to rewrite the equation in the form x/a + y/b = 1.
To do this, move all the constant terms to the right side, and all the
x- and y-terms to the left side. Divide both sides by the constant on
the right to make it equal to 1. Gather like terms, then set a to be
the reciprocal of the x-coefficient and b the reciprocal of the
y-coefficient.  In this case, we are part way there with the equation

2*x - 3*y = -5.

Divide both sides by -5 (i.e. divide by the equation -5 = -5). Then

(2*x - 3*y)/(-5) = (-5)/(-5)

or

(-2/5)*x + (3/5)*y = 1

or

x/(-5/2) + y/(5/3) = 1.

The right side is 1 as desired for this form of the equation of the
line.  From this form you can read off a = -5/2 and b = 5/3. These
are the x-intercept (a,0) and y-intercept (0,b) of the line. From
these two points it is easy to draw the line.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search