Directly Proportional Vs. Linear

Tickets People

3 1

6 2

9 3

12 4

Tickets People

3 2

6 3

9 4

12 5

EQUATION y=kx

TABLE TABLE

EQUATION y=mx + b

543210

0 3 6 9 12

PEOPLE

TICKETS

PEOPLE

543210

0 3 6 9 12TICKETS

Directly ProportionalTickets People

3 1

6 2

9 3

12 4

EQUATIONy=kxx

TABLE

543210

0 3 6 9 12

PEOPLE

TICKETS

• Both variables increase at a Constant (k) Rate .

• Divide y & x to find a Constant (k) in order to test for Directly Proportional Relationships within a table.

• Only 2 items in the relationship.

• Starts at the origin.

Linear Relationship

• Check to see if table has a pattern, but DOES NOT divide to give a Constant (k).

• DOES NOT start at the origin.

• Has an extra variable/flat rate.

• Starts at the y-intercept.

Tickets People

3 2

6 3

9 4

12 5

GRAPH

EQUATION y=mx + b

PEOPLE

543210

0 3 6 9 12TICKETS

Graph/Table Linear Equation

Nachos $ (Money)

0 4

2 10

4 16

6 22

• Table

$

Nachos

2220181614121086420

0 2 4 6

Inversely Proportional

Miles Hours

120 1

60 2

40 3

30 4

GRAPH

EQUATION

5 4 3 2 1 0 10 20 30 40 50 60 70 80 90 100 110 120

• X variable increase, Y variable decreases or Vice Versa at a Constant (k) Rate.

• Multiply x & y in the table to find a Constant (k) to test for Inversely Proportional

NonLinear

• Tables have NO Pattern• Graph not straight line.• Equation has exponent.

– 50

TABLESFlow Chart for Testing

BAGS APPLES

1 7

2 11

3 15

4 19

CHECK FOR SLOPE/PATTERN

YES NO

CHECK RATIOS

ALL RATIOS EQUAL

RATIOS NOT EQUAL

DIRECT LINEAR

MULTIPLY X & Y

(K) CONSTANT ALL THE SAME

(K) CONSTANT NOT THE SAME

INVERSE NONLINEAR

Practice

X Y

2 5

4 10

6 15

8 20

1) 3)

2) 4)

X Y

2 24

4 12

6 8

8 6

X Y

1 6

2 10

3 14

4 18

X Y

1 2

3 5

5 12

7 18

Directly Proportional? Linear? Nonlinear? Inversely proportional?

Practice

Miles traveled Cost of gas

25 $5

50 $10

75 $15

100 $20

1) 3)

2) 4)Miles traveled Cost of gas

25 $5

50 $10

75 $15

100 $20

30 2

60 1

90

Miles traveled Cost of gas

CHECK FOR PATTERN

YES NO

CHECK RATIOS

ALL RATIOS EQUAL

RATIOS NOT

EQUAL

Directly Proportional

LINEAR

MULTIPLY X & Y

(K) CONSTANT ALL THE SAME

(K) CONSTANT NOT THE SAME

NONLINEARInversely Proportional

YES NO

Draw these and fill these in on the quiz!!!

Review for quizTell if each table is linear, nonlinear, directly proportional, or inversely proportional.

1) 2)

3) 4)

X Y

1 24

2 12

3 8

6 4

X Y

30 4

60 8

90 12

120 4

X Y

5 20

10 40

15 60

20 80

X Y

5 11

6 13

7 15

8 17

Review for quizTell if each equation is linear, nonlinear, directly

proportional, or inversely proportional and WHY.1) y = -7x – 52) y= 3) y = 45x4) y = -2x²5) y = 5x + 86) y =

Practice

Practice