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
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