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5.6 Direct Variation Notes.notebook Algebra Lesson 5.6 Today's learning target: December 17, 2013 A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings. Students will be able to identify, write, and graph direct variation. The equation y = 5x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of rice. MN Standards: 7th Grade Standard (previous course) Example 1A: Identifying Direct Variations from Equations Tell whether the equation represents a direct variation. If so, identify the constant of variation. y = 3x This equation represents a direct variation because it is in the form of y = kx. The constant of variation is 3. A direct variation is a special type of linear relationship that can be written in the form y = kx, where k is a nonzero constant called the constant of variation. Example 1B: Tell whether the equation represents a direct variation. If so, identify the constant of variation. 3x + y = 8 This equation is not a direct variation because it cannot be written in the form y = kx. 1 5.6 Direct Variation Notes.notebook Example 1C: Tell whether the equation represents a direct variation. If so, identify the constant of variation. December 17, 2013 Try It Out! Tell whether the equation represents a direct variation. If so, identify the constant of variation. 3y = 4x + 1 3x = –4y y + 3x = 0 What happens if you solve y = kx for k? Example 2A: Identifying Direct Variations from Ordered Pairs Tell whether the relationship is a direct variation. Explain. Method 1 Write an equation. y = 3x This is direct variation because it can be written as y = kx, where k = 3. 2 5.6 Direct Variation Notes.notebook December 17, 2013 Try It Out! Example 2a Tell whether the relationship is a direct variation. Explain. Example 2B: Tell whether the relationship is a direct variation. Explain. Method 1 Write an equation. y = x – 3 This is not a direct variation because it cannot be written as y = kx. Example 2b Tell whether the relationship is a direct variation. Explain. Example 2c Tell whether the relationship is a direct variation. Explain. Example 4: Graphing Direct Variations A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph. Example 3: Writing and Solving Direct Variation Equations Step 1 Write a direct variation equation. The value of y varies directly with x, and y = 3, when x = 9. Find y when x = 21. Method 1 Find the value of k and then write the equation. Step 2 Choose values of x and generate ordered pairs. Method 2 Use a proportion. Step 3 Graph the points and connect. 3 5.6 Direct Variation Notes.notebook December 17, 2013 Algebra Lesson 5.6 Today's learning target: Students will be able to identify, write, and graph direct variation. HW: 5.6 #10-17, 20-44 evens, 47-55 p339-341 MN Standards: 7th Grade Standard (previous course) 4