1. Algebra-II Honors/Gifted @
Sections 2-2 and 8-1 :
Variation

2. Do I Have to Mow the Whole Thing?
Imagine you’ve been asked to mow a rectangular garden that is 24 square yards. In your mind, you probably have an idea of the dimensions of the garden from this description.

3. Sketch a rectangle whose area is 24 square units and label its dimensions. Sketch another rectangle with the same area but different dimensions.
length
1.5
0.5
120
0.3
width

4. Graph a scatter plot using graphing calculator
Graph a scatter plot using graphing calculator! If you were to connect the points, how would you describe the graph of the function? As the length increases, the width ___________ As the length decreases, the width ___________ What equation represents this relationship? Use this function to fit your data.

5. Direct Variation
y = kx or
Inverse Variation
y = 𝒌 𝒙 or k = xy

6. Direct variation Neither Inverse variation
Determine the relationship between the values in each table is a direct variation, an inverse variation or neither. 1 x .5 5 8 12 15 y
.125
1.25 2 3
3.75
y = 𝟏 𝟒 𝒙
Direct variation
Function: 2 x
1.5 4
7.5 10 13 y
8.5 16
26.5 34 43
Neither 3 x
.25 2 3 5 8 y 28
3.5
2.33
1.4
.875
y = 𝟕 𝒙
Function:
Inverse variation

7. ALGEBRA II HONORS/GIFTED - SECTION 8-1 (Inverse Variation)
12/1/2018
Combined Variations
If one quantity varies directly with two or more quantities, we have joint variation. z varies jointly with x and y, z = kxy If one quantity varies with two or more quantities, we have combined variation. z varies directly with x and inversely with the product uy, z = 𝒌𝒙 𝒖𝒚

8. 4. Suppose z varies jointly with x and y.
a) Write the function that models this variation when x = 6, y = 9, and z = 162.
b) Find z when x = 5 and y = 7.

9. Can you just move two lines and form seven squares?