Question 120986
How would I graph these equations: (a) y = x + 3
:
Choose some values for x, let's use 3 values: x = -3; x = 0; x = +3
(You actually only need two for linear equations)
:
We are going to substitute each value in the above equation to find y:
For x = -3:
y = (-3) + 3
y = 0
:
For x = 0:
y = (0) + 3
y = 3
:
For x = +3
y = (3) + 3
y = 6
:
Make an x/y table from the above values
 x | y
-------
-3 | 0
 0 |+3
+3 | 6
:
Plot each of these x/y values and join them with a straight line
You graph should look like this
:
{{{ graph( 300, 200, -6, 5, -8, 8, x+3) }}} 

:
:
(b) y = -1/3x; use the the same x values for this one, find y
For x -3
y = -1/3(-3)
y = +1
:
For x = 0
y = -1/3(0)
y = 0
:
For x =+3
y = -1/3(3)
y = -1 
:
Make an x/y table from the above values
 x | y
-------
-3 |+1
 0 | 0
+3 |-1
Plot these x/y values, you graph should look like this:
{{{ graph( 300, 200, -6, 5, -4, 4, (-1/3)x) }}} 


(c) y = 1/3x y; use the the same x values for this one, find y
For x -3
y = 1/3(-3)
y = -1
:
For x = 0
y = 1/3(0)
y = 0
:
For x =+3
y = 1/3(3)
y = +1 
:
Make an x/y table from the above values
 x | y
-------
-3 |-1
 0 | 0
+3 |+1
Plot these x/y values, you graph should look like this:
{{{ graph( 300, 200, -6, 5, -4, 4, (1/3)x) }}} 
:
:
(d) y = 3x; use the the same x values for this one, find y
For x -3
y = 3(-3)
y = -9
:
For x = 0
y = -3(0)
y = 0
:
For x =+3
y = 3(3)
y = +9 
:
Make an x/y table from the above values
 x | y
-------
-3 |-9
 0 | 0
+3 |+9
Plot these x/y values, you graph should look like this:
{{{ graph( 300, 200, -6, 5, -10, 10, 3x) }}}
:
Note that I changed the scale of the graphs slightly to improve the illustration. 
You can do all these on standard -10,+10 scale graph paper
:
Did this enlighten you to the graphing world? Any questions?