Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.
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Transcript of Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.
![Page 1: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/1.jpg)
Proportional & Nonproportional Relationships
![Page 2: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/2.jpg)
RECALL: Direct Variation y = kx
![Page 3: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/3.jpg)
RECALL: Direct Variation y = kx
Proportional Relationships – direct variation(passes through origin)
![Page 4: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/5.jpg)
Ex. 1 Write an equation in function notation for the graph.
![Page 6: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/6.jpg)
Ex. 1 Write an equation in function notation for the graph.
x y
![Page 7: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/7.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
![Page 8: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/8.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
0 0
![Page 9: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/9.jpg)
Ex. 1 Write an equation in function notation for the graph.x y-1 -2
0 01 2
![Page 10: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/html5/thumbnails/17.jpg)
Ex. 2 Write an equation in function notation for the graph.
![Page 18: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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: Proportional & Nonproportional Relationships. RECALL: Direct Variation y = kx.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bffa1a28abf838cc01d0/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