Recognizing and Interpreting Linear Relationship s Sara Salefske
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Recognizing and Interpreting
Linear Relationships
Sara Salefske
Linear Relationships
Definition: A set of directly proportional points, that
when placed on a graph, create a straight line.
How to Tell if it is Linear
Figure out a common way to get from each X-value to their corresponding Y-values.
There are 4 easy steps to help you out.
1. Start with the first X-value and the first Y-value.
1. Take all possible relationships into consideration.
How to Tell (cont.)
Example:
The first pair, (2,10) could have the possible formulas of :
y=x+8, y=(x+3)2, y=2x+6, etc.
X Y
2 10
3 12
4 14
5 16
How to Tell (cont.)
1. Use one of the possible relationships on the next pair of numbers.
1. If the same formula works for each set, it is linear.
**If there is no common formula for each set, it is NOT linear.
Your Turn: Tables
X Y
5 30
6 36
7 42
8 48
X Y
12
7
13
60
14
5
15
14
X Y
2 0
3 4
4 8
5 12
X Y
10
14
11
15
12
16
13
17
It's your turn. Which tables, if any show linear relationships? Write on scrap paper which ones you think are, and a formula that would solve them.
A B C D
Your Turn: Tables
X Y
5 30
6 36
7 42
8 48
X Y
2 0
3 4
4 8
5 12
X Y
10
14
11
15
12
16
13
17
X Y
10
14
11
15
12
16
13
17
X Y
12
7
13
60
14
5
15
14
A. Not a linearRelationship.
B. 6x=y C. (x-2)4=yOr
4x-8=y
D. x+4=y
Now Learn to Use Graphs
1. Find easy points on the line.
2. Using these points/pairs, make a table.
**Also: if the graph is a line, it is a linear relationship, but some graphs are distorted, so be sure to pick some points to double check.
Example Graph
X Y
2 10
3 12
4 14
5 16
0 1 2 3 4 5
16
14
12
10
8
1. Set up a table using the points from the graph
2. Next find possible formulas.
Example Graph
0 1 2 3 4 5
16
14
12
10
8
3. Do any of the formulas from step 2 work for every pair?
2x+6=y
**Always check your work.
4. If they all have the same relationship, it is a linear relationship. If not, its NOT linear.
Drawing Graphs From Tables and Formulas
1. Using a given formula, plug numbers in for x, and solve for y to create a table.
2. Using a given table, or a table created in step 1, plot the points on a graph.
3. Using the graph, determine if the relationship is a linear relationship.
Interpreting Formulas
1. If given formula fits slope-intercept form (y=mx+b), it is linear.
2. b is equal to the y-intercept.
3. y-intercept tells where a linear relationship would cross the y-axis.
Your turn: Formulas
Which are linear relationships, if any, and what are their y-intercepts (b values) for those formulas?
A. y=4x+3 B. x=y2+2
C. y=2x2 D. y=3
E. (y+2)/3 =x F. x=1
Your Turn: Formulas
A. y=4x+3 y=4x+3 3
B. x=y2+2 not linear
C. y=2x2 not linear
D. y=3 y=0x+3 3
E. (y+2)/3 =x y=3x-2 -2
F. x=1 not linear
Formulas y=mx+b form b-value
Review
1. What is the linear relationship in y=mx+b form?
X Y
2 4
3 7
4 10
5 13
Review
0 1 2 3 4 5
4
3
2
1
0
2. What is the linear relationship in slope-intercept form?
3. What is the y-intercept (b-value)?y+6=x 4
Review
4. Make a table from the following formula:
y=2(x+4)
5. Create a graph from this formula:
3+y=4x
6. Create a graph from this table:X Y
-1 1
0 4
1 7
2 10
Related Documents
