3.6 – Proportional & Nonproportional Relationships.
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Transcript of 3.6 – Proportional & Nonproportional Relationships.
![Page 1: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/1.jpg)
3.6 – Proportional & Nonproportional Relationships
![Page 2: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/2.jpg)
RECALL: Direct Variation y = kx
![Page 3: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/3.jpg)
RECALL: Direct Variation y = kx
Proportional Relationships – direct variation(passes through origin)
![Page 4: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/4.jpg)
RECALL: Direct Variation y = kx
Proportional Relationships – direct variation(passes through origin)
Nonproportional Relationships – any linear function that cannot be expressed by y = kx
![Page 5: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/5.jpg)
Ex. 1 Write an equation in function notation for the graph.
![Page 6: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/6.jpg)
Ex. 1 Write an equation in function notation for the graph.
x y
![Page 7: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/7.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
![Page 8: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/8.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
0 0
![Page 9: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/9.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
0 01 2
![Page 10: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/10.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
0 01 22 4
![Page 11: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/11.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
0 01 22 4
![Page 12: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/12.jpg)
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
![Page 13: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/13.jpg)
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
![Page 14: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/14.jpg)
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
![Page 15: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/15.jpg)
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
![Page 16: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/16.jpg)
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
![Page 17: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/17.jpg)
Ex. 2 Write an equation in function notation for the graph.
![Page 18: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/18.jpg)
Ex. 2 Write an equation in function notation for the graph.
x y-1 -3
0 -11 12 3
![Page 19: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/19.jpg)
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
![Page 20: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/20.jpg)
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
![Page 21: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/21.jpg)
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
![Page 22: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/22.jpg)
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
![Page 23: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/23.jpg)
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
![Page 24: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/24.jpg)
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
![Page 25: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/25.jpg)
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
![Page 26: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/26.jpg)
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
![Page 27: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/27.jpg)
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
![Page 28: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/28.jpg)
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
![Page 29: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/29.jpg)
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
![Page 30: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/30.jpg)
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
![Page 31: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/31.jpg)
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
![Page 32: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/32.jpg)
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
![Page 33: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/33.jpg)
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
![Page 34: 3.6 – Proportional & Nonproportional Relationships.](https://reader034.fdocuments.net/reader034/viewer/2022052122/56649edc5503460f94bec05f/html5/thumbnails/34.jpg)
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