3.6 – Proportional & Nonproportional Relationships

3.6 – Proportional & Nonproportional Relationships

RECALL: Direct Variation y = kx

RECALL: Direct Variation y = kx

Proportional Relationships – direct variation(passes through origin)

RECALL: Direct Variation y = kx

Proportional Relationships – direct variation(passes through origin)

Nonproportional Relationships – any linear function that cannot be expressed by y = kx

Ex. 1 Write an equation in function notation for the graph.

Ex. 1 Write an equation in function notation for the graph.

x y

Ex. 1 Write an equation in function notation for the graph.x y-1 -2

Ex. 1 Write an equation in function notation for the graph.x y-1 -2

0 0

Ex. 1 Write an equation in function notation for the graph.x y-1 -2

0 01 2

Ex. 1 Write an equation in function notation for the graph.x y-1 -2

0 01 22 4

Ex. 1 Write an equation in function notation for the graph.x y-1 -2

0 01 22 4

Ex. 1 Write an equation in function notation for the graph.

Goes through origin so direct variation & proportional

x y-1 -2

0 01 22 4

Ex. 1 Write an equation in function notation for the graph.

Goes through origin so direct variation & proportional

x y-1 -2

0 01 22 4

+1

+1

+1

Ex. 1 Write an equation in function notation for the graph.

Goes through origin so direct variation & proportional

x y-1 -2

0 01 22 4

+1

+1

+1

+2

+2

+2

Ex. 1 Write an equation in function notation for the graph.

Goes through origin so direct variation & proportional

y = 2x

x y-1 -2

0 01 22 4

+1

+1

+1

+2

+2

+2

Ex. 1 Write an equation in function notation for the graph.

Goes through origin so direct variation & proportional

y = 2xf(x) = 2x

x y-1 -2

0 01 22 4

+1

+1

+1

+2

+2

+2

Ex. 2 Write an equation in function notation for the graph.

Ex. 2 Write an equation in function notation for the graph.

x y-1 -3

0 -11 12 3

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

x y-1 -3

0 -11 12 3

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

x y-1 -3

0 -11 12 3

+1

+1

+1

+2

+2

+2

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

x 2x y-1 -3

0 -11 12 3

+1

+1

+1

+2

+2

+2

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

x 2x y-1 -2 -3

0 0 -11 2 12 4 3

+1

+1

+1

+2

+2

+2

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

y = 2x

x 2x y-1 -2 -3

0 0 -11 2 12 4 3

+1

+1

+1

+2

+2

+2

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

y = 2x

x 2x y-1 -2 -3

0 0 -11 2 12 4 3

+1

+1

+1

+2

+2

+2

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

y = 2x

x 2x y-1 -2 -3

0 0 -11 2 12 4 3

+1

+1

+1

+2

+2

+2

-1

-1

-1

-1

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

y = 2x – 1

x 2x y-1 -2 -3

0 0 -11 2 12 4 3

+1

+1

+1

+2

+2

+2

-1

-1

-1

-1

Ex. 2 Write an equation in function notation for the graph.

DOES NOT GO through originso Nonproportional

y = 2x – 1 f(x) = 2x – 1

x 2x y-1 -2 -3

0 0 -11 2 12 4 3

+1

+1

+1

+2

+2

+2

-1

-1

-1

-1

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

a. Write an equation for the data.

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

a. Write an equation for the data.

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

+1 +1 +1

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

a. Write an equation for the data.

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

+1 +1 +1

+1.65 +1.65 +1.65

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

a. Write an equation for the data.y = 1.65x

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

+1 +1 +1

+1.65 +1.65 +1.65

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

a. Write an equation for the data.y = 1.65x

b. Describe the relationship between the hour and inches of snowfall.

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

+1 +1 +1

+1.65 +1.65 +1.65

Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.

a. Write an equation for the data.y = 1.65x

b. Describe the relationship between the hour and inches of snowfall.

Proportional

Hour 1 2 3 4

Inches of Snowfall 1.65 3.30 4.95 6.60

+1 +1 +1

+1.65 +1.65 +1.65