Graphing Linear Equations in Two Variables
Examples
1. Graph 2x + 3y = 7.
Look at the coefficients and note that if we choose a sequence of odd integers
as replacement
for y-values, such as: { -3, -1, 1, 3, 5}, the resulting x-sequence will be integers
Build a table for 2x + 3y = 7.
| 2x + 3y = 7 Let y = 1
2x + 3( 1) = 7 or x = 2
repeat for y = 3
2x + 3( 3) = 7, or x = - 1 |
Put these values in the
middle of the table, then
write the “common
differences” for both x
and y .
Use the value for dx to
complete the table
values for x.
Note the value for dy in
the table values for y. |
 For complete table see below. |
| Note adding ± 3 to given x-values
forms an arithmetic sequence.
Note adding
 2 to given y-values
forms an arithmetic sequence.
To be sure you should always check the “outer points”.
|
For complete table see below.
 |
Check:
Check:
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|
|
Check the dy and dx on your graph. |
 |
Plot the points, draw line:
 |
For other examples study the coefficients for combinations that will yield integer points (x1, y1).
2. 3x + 5y = 7
Since 10 − 3 = 7, choose x = -1
and y = 2 to satisfy this difference.
3( -1) + 5( 2) = 7 (-1, 2)
Repeat for the another pair of numbers
| Since 5 + 7 = 12, choose y = -1
and solve for x.
Note adding
 5 to given
x-values and ± 3 to given y-values forms
an arithmetic sequence for each. |
Put these values in the
middle of the table,
then write their “common differences”
for as dx and dy .
Use the value for dx to
complete the table
values for x.
and
dy to complete the
table values for y.
NOTE: Opposite signs
above given values.
|
 |
| To be sure you should always check the “outer points”.
|
Check:
Check:
Check the dy and dx on your graph. |
Plot the points, draw line:
 |
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