Alg II 2-2 Direct Variation


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Alg II 2-2 Direct Variation

  1. 1. Algebra II Chapter 2 Functions, Equations, and Graphs© Tentinger
  2. 2.  Essential Understanding: some quantities are in a relationship where the ratio of corresponding values is constant Objectives:  Students will be able to write and interpret direct variation equations
  3. 3.  Algebra A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-BF.1. Write a function that describes a relationship between two quantities.★ Determine an explicit expression, a recursive process, or steps for calculation from a context.
  4. 4.  You are building a roof. You mark off four equal intervals from along the base and place vertical posts as shown below. What are the heights of the four vertical posts? Explain. How are the base and height of the largest triangle related? How can you find the height of the smallest triangle? What is the relationship between each post?
  5. 5.  In an equation, as the input increases or decreases, the output increases or decreases proportionally y = kx, where k ≠ 0 and x represents input values and y represents the output values K is called the constant of variation How could you find k if you know x and y?
  6. 6.  Determine if there is a direct relationship, if so what is the constant of variation?
  7. 7.  For each function determine if y varies directly with x. If so, what is the constant of variation? 5x + 3y = 0 y = x/9
  8. 8.  Suppose y varies directly with x, and y = 15 when x = 3. What is why when x = 12? What do you need to find first? The number of Calories varies directly with the mass of cheese. If 50 grams of cheese contains 200 Calories, how many Calories are in 70 grams of cheese?
  9. 9.  y = (-2/3)x y = 3x
  10. 10.  Pg. 71 #8 – 36 even 15 problems