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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
