2-2 Direct Variation

Algebra II Chapter 2 Functions, Equations, and Graphs© Tentinger

Essential Understanding and Objectives

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

Iowa Core Curriculum

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.

Warm Up

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?

Direct Variation

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?

Example

Determine if there is a direct relationship, if so what is the constant of variation?

Example

For each function determine if y varies directly with x. If so, what is the constant of variation?

5x + 3y = 0

y = x/9

Example

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?

Graph each direct variation

y = (-2/3)x

y = 3x

Homework

Pg. 71 #8 – 36 even 15 problems