4 5 Direct Variation 4 5 Direct Warm

4 -5 Direct Variation Warm Up Solve for y. 1. 3 + y =

4 -5 Direct Variation Objective Identify, write, and graph direct variation. Holt Mc. Dougal

4 -5 Direct Variation A recipe for paella calls for 1 cup of rice

4 -5 Direct Variation Vocabulary A direct variation is a special type of linear

4 -5 Direct Variation Example: Identifying Direct Variations from Equations y = 3 x

4 -5 Direct Variation Example 3 x + y = 8 – 3 x

4 -5 Direct Variation Example – 4 x + 3 y = 0 +4

4 -5 Direct Variation I do…… Does the equation represents a direct variation? If

4 -5 Direct Variation We do…… Does the equation represents a direct variation? If

4 -5 Direct Variation You do…… y + 3 x = 0 – 3

4 -5 Direct Variation Example: Identifying Direct Variations from Ordered Pairs 6 = __2

4 -5 Direct Variation Example: Continued Another way of getting k is by dividing

4 -5 Direct Variation Example Solve for K if it is a direct variation.

4 -5 Direct Variation Check It Out! Example 2 a This is not direct

4 -5 Direct Variation Example 3: Writing and Solving Direct Variation Equations The value

4 -5 Direct Variation Example 3 Continued The value of y varies directly with

4 -5 Direct Variation Lesson Quiz: Tell whether each equation represents a direct variation.

4 -5 Direct Variation Lesson Quiz: Part I Tell whether each equation represents a

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4 -5 Direct. Variation 4 -5 Direct Warm Up Lesson Presentation Lesson Quiz Holt 1 Algebra Holt. Algebra Mc. Dougal Algebra 11 Mc. Dougal

4 -5 Direct Variation Warm Up Solve for y. 1. 3 + y = 2 x Solve for x. 2. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Warm Up Solve for y. 1. 3 + y = 2 x – 3 Solve for x. 2. 9 Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Objective Identify, write, and graph direct variation. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation A recipe for paella calls for 1 cup of rice to make 5 servings. Above is described by the equation: y = 5 x Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Vocabulary 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. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example: Identifying Direct Variations from Equations y = 3 x This equation represents a direct variation because it is in the form of y = kx. The constant of variation is 3. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example 3 x + y = 8 – 3 x y = – 3 x + 8 This equation is not a direct variation because it cannot be written in the form y = kx. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example – 4 x + 3 y = 0 +4 x 3 y = 4 x This equation represents a direct variation because it is in the form of y = kx. The constant of variation is. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation I do…… Does the equation represents a direct variation? If so, identify the constant of variation. 3 y = 4 x + 1 not a direct variation Holt Mc. Dougal Algebra 1

4 -5 Direct Variation We do…… Does the equation represents a direct variation? If so, identify the constant of variation. 3 x = – 4 y Solve the equation for y. – 4 y = 3 x Since y is multiplied by – 4, divide both sides by – 4. Yes, it is a direct variatopm. The constant of variation is. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation You do…… y + 3 x = 0 – 3 x y = – 3 x Yes, it is a direct variation. The constant of variation is – 3. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example: Identifying Direct Variations from Ordered Pairs 6 = __2 Multiply 2 with 3! y = 3 x This is direct variation, where k = 3. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example: Continued Another way of getting k is by dividing y by x. K = y/x Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example Solve for K if it is a direct variation. … This is not direct variation coz K is not constant! Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Check It Out! Example 2 a This is not direct variation. Holt Mc. Dougal Algebra 1

4 -5 Direct Variation Example 3: Writing and Solving Direct Variation Equations 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. y = kx Write the equation for a direct variation. 3 = k(9) Substitute 3 for y and 9 for x. Solve for k. Since k is multiplied by 9, divide both sides by 9. The equation is y = Holt Mc. Dougal Algebra 1 x. When x = 21, y = (21) = 7.

4 -5 Direct Variation Example 3 Continued The value of y varies directly with x, and y = 3 when x = 9. Find y when x = 21. Method 2 Use a proportion. In a direct variation is the same for all values of x and y. 9 y = 63 y=7 Holt Mc. Dougal Algebra 1 Use cross products. Since y is multiplied by 9 divide both sides by 9.

4 -5 Direct Variation Lesson Quiz: Tell whether each equation represents a direct variation. If so, identify the constant of variation. 1. 2 y = 6 x 2. 3 x = 4 y – 7 Tell whether each relationship is a direct variation. Explain. 3. Holt Mc. Dougal Algebra 1 4.

4 -5 Direct Variation Lesson Quiz: Part I Tell whether each equation represents a direct variation. If so, identify the constant of variation. 1. 2 y = 6 x yes; 3 2. 3 x = 4 y – 7 no Tell whether each relationship is a direct variation. Explain. 3. Holt Mc. Dougal Algebra 1 4.