# Finding rule for linear or Quadratic patterns

```Looking for Rules in a Table
Finding a Linear Rule from a table
The general Linear Equation is
y = mx + c
m
c
= the y -intercept
Example One
x
y
-2
1
-1
2
0
3
1
4
2
5
3
6
Step One:
Check to see if our top row is in order from smallest to
largest. If not create a new table and arrange in order
Step Two:
Find the difference the x values are going up or down by.
(arrows on table above)
Step Three:
Find the difference the y values are going up or down
by.(arrows on table above)
Step Four:
To find the Constant multiplier (gradient) we take the y
value difference and divide it by the x value difference.
Step Five: Now we need to fond the y-intercept
a)
we can look at the column where x = 0 and find the
corresponding y-value. This is the y-intercept
b)
If we don’t have x = 0 we can choose a point to
substitute in to find the c value (y-intercept
Example Two:
a
b
-3
-4
Example Three:
t
w
2
-3
Example Four:
p
m
-4
4
Find the rule from the table
-2
-1
-1
2
0
5
1
8
2
11
5
0
6
1
7
2
2
-8
4
-12
Find the rule from the table
3
-2
4
-1
Find the rule from the table
-2
0
0
-4
Finding a Quadratic Rule from a table
2
y = ax + bx + c
a = half of the second difference
c = the y –intercept
b is found using substitution
Example One
x
y
-2
5
-1
2
0
1
1
2
2
5
3
10
Step One:
Check to see if our top row is in order from smallest to
largest. If not create a new table and arrange in order
Step Two:
Find the first difference the y values are going up or down
by. (arrows on table above)
Step Three:
If the first deifference are not the same then the equation is
not linear. Now do a second difference.
Step Four:
If the second difference is the same then it is a quadratic
equation.
Step Five:
The a value is half of this second difference.
Step Six:
Determine the c value. This is the y value when x = 0 in our
table.
Step Seven:
Choose a point to substitute into our equation to find our b
value.
Example Two:
a
b
-3
8
Example Three:
t
w
2
5
Example Four:
x
y
-2
15
Find the rule from the table
-2
4
-1
2
0
2
1
4
2
8
5
29
6
41
7
54
1
0
2
-1
Find the rule from the table
3
11
4
19
Find the rule from the table
-1
8
0
3
For all of the tables below:
 Find if there is any relationship or pattern
 If there is a pattern what type of graph is it Linear or Quadratic or neither
 If there is a linear or quadratic graph what is the equation of that graph
x
y
1
-31
2
-28
3
-25
4
-22
5
-19
6
-16
7
-13
8
-10
9
-7
x
y
1
12
2
6
3
4
4
3
5
2.4
6
2
7
1.71
8
1.5
9
1.33
x
y
-3
14
-2
9
-1
6
0
5
1
6
9
3
14
x
y
4
4
5
6
6
8
7
10
8
12
9
14
10
16
2
11
18
x
y
-5
4
-4
9
x
y
-4
-16
x
y
1
4
2
6
3
8
6
14
7
16
x
y
2
5
3
13
4
23
5
35
6
49
-3
-9
-3
16
-2
-4
-2
25
-1
-1
-1
36
0
0
0
49
1
1
7
65
1
64
2
4
2
81
```