Direct, Inverse, and Joint Variation in Pre-Calculus

Jan 09, 2025

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Learn about direct, inverse, and joint variation in pre-calculus with formulas and examples. Understand the relationships between variables y and x in different scenarios to solve problems effectively.

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Direct, Inverse, and Joint Variation in Pre-Calculus

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3-8 Direct, Inverse, and Joint Variation Pre Calc A
Formulas • Direct y = kx • Inverse • Joint y = kxz
Ex 17: • Suppose y varies directly as x and y = 45 when x = 2.5. Find the constant of variation and then find y when x = 4.
Ex : • If y varies inversely as the square root of x and y = 20 when x = 49, find x when y = 10.
Ex last one: • If y varies jointly as x and z and y = 5 when x = -4 and z = -2, find y when x = -6 and z = -3.

DIRECT & INVERSE VARIATION

DIRECT & INVERSE VARIATION. Can you distinguish between the two?. Description. Two related quantities can vary in one of two ways: directly or inversely In direct variation, as one quantity increases, so does the other.

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Direct and Inverse Variation Functions

Direct and Inverse Variation Functions. Learning Goal 4.3. Direct Variation. Two variables, x and y, vary directly if there is a nonzero number k such that y=kx Just because one quantity increases when the other increases does not mean x and y vary directly

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Inverse and Joint Variation

Inverse and Joint Variation. Section 9.1. What You Will Learn:. How to write and use inverse variation models. How to write and use joint variation models.

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9.1: Inverse and Joint Variation

9.1: Inverse and Joint Variation. Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models. Review of Direct Variation:. Linear function whose graph passes through the origin y= kx , where k is the constant of variation

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Direct and Inverse Variation

Direct and Inverse Variation. Investigation #1 Ramp height and length vs time. Direct vs Indirect. “ y varies directly as x " means… y = kx What does that graph look like? “ y varies inversely as x " means… y = k/x What does that graph look like? What is k?

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Direct, Inverse and Joint Variation

Direct, Inverse and Joint Variation. December 10 Yes, this is where I really want to be. Direct Variation. A direct variation is a linear function that can be written in the form y= kx . Where k ≠ 0. The two variable ( x & y ) vary directly or are proportional.

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Direct and Inverse Variation

Direct and Inverse Variation. Algebra I. Direct Variation. When the line passes through the origin. When y increases, x increases. Equation: y = kx , where k 0. Constant of variation – k Say “ y varies directly with x”. Identifying the constant of variation. y = 6x

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Direct Variation & Inverse Variation (SOL A.8)

Direct Variation & Inverse Variation (SOL A.8). Chapters 5-2 & 11-6. Direct Variation. If the ratio between two variables is a constant, than a direct variation exists. A direct variation can be written in the form of y = kx , where k is the constant of variation. . Inverse Variation.

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Direct and Inverse Variation

Objectives: Use direct and inverse variation. Direct and Inverse Variation. Variation. Direct variation: y varies directly with x Inverse variation: y varies inversely with x The number is the constant of variation. EX: Solve the variation problem.

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8-1: Model Joint and Inverse Variation

8-1: Model Joint and Inverse Variation. Objectives: Identify inverse and direct variation equations. Solve for the constant in variation equations. Common Core Standards: A-REI-2 Assessments: Define all vocab for this section Do worksheet 8-1.

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Direct Variation  Inverse Variation 

8.1 Model Inverse and Joint Variation. By the end of the lesson you should: classify direct and inverse variations write an inverse variation equation Write and inverse variation model write a joint variation equation compare variations. Direct Variation  Inverse Variation .

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direct variation inverse variation constant of variation joint variation combined variation

Vocabulary. direct variation inverse variation constant of variation joint variation combined variation. Notes.

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9.1 Inverse and Joint Variation

9.1 Inverse and Joint Variation. Goal: Use inverse variation and joint variation models. Warm-up. Simplify:. Inverse Variation. 2 variables, x and y, vary inversely if: k is called the constant of variation. Example 1.

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1.10 Direct Variation and Inverse Variation

1.10 Direct Variation and Inverse Variation. Direct Variation. y varies directly as x y is directly proportional to x y = kx k is the constant of proportionality. Inverse Variation. y varies inversely as x y is inversely proportional to x. Ex. Find a mathematical model representing

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DIRECT, INVERSE, AND JOINT VARIATION

DIRECT, INVERSE, AND JOINT VARIATION. Unit 3 English Casbarro. If y varies directly as x and y = 14, when x = 3.5, find k and write and graph the variation. Notice that the direct variation graph always intersects the coordinate plane at the origin. Try this: If y varies

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3.8 – Direct, Inverse, and Joint Variation

3.8 – Direct, Inverse, and Joint Variation. Direct Variation. When two variables are related in such a way that the ratio of their values remains constant. “y varies directly as x” would simply mean as x increases – so does y. Or as x decreases – so does y.

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Inverse, Joint, and Combined Variation

Inverse, Joint, and Combined Variation. Objective: To find the constant of variation for many types of problems and to solve real world problems. Inverse Variation.

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direct variation constant of variation joint variation inverse variation

Helpful Hint. If k is positive in a direct variation, the value of y increases as the value of x increases. Vocabulary. direct variation constant of variation joint variation inverse variation. You can use algebra to rewrite variation functions in terms of k.

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DIRECT, INVERSE, AND JOINT VARIATION

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Identify direct and inverse variation

Because xy = 4 can be written in the form y = , xy = 4 represents inverse variation. The constant of variation is 4. a. x. y =. 4. x. EXAMPLE 1. Identify direct and inverse variation. Tell whether the equation represents direct variation , inverse variation , or neither.

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Direct, Inverse, and Joint Variation in Pre-Calculus

Direct, Inverse, and Joint Variation in Pre-Calculus

Presentation Transcript

DIRECT &amp; INVERSE VARIATION

Direct and Inverse Variation Functions

Inverse and Joint Variation

9.1: Inverse and Joint Variation

Direct and Inverse Variation

Direct, Inverse and Joint Variation

Direct and Inverse Variation

Direct Variation &amp; Inverse Variation (SOL A.8)

Direct and Inverse Variation

8-1: Model Joint and Inverse Variation

Direct Variation  Inverse Variation 

direct variation inverse variation constant of variation joint variation combined variation

9.1 Inverse and Joint Variation

1.10 Direct Variation and Inverse Variation

DIRECT, INVERSE, AND JOINT VARIATION

3.8 – Direct, Inverse, and Joint Variation

Inverse, Joint, and Combined Variation

direct variation constant of variation joint variation inverse variation

DIRECT, INVERSE, AND JOINT VARIATION

Identify direct and inverse variation

DIRECT & INVERSE VARIATION

Direct Variation & Inverse Variation (SOL A.8)