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

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

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.

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

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.

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

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

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

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.

Can you just move two lines and form seven squares?