Model Inverse and Joint Variation

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Presentation transcript:

Model Inverse and Joint Variation Notes 9.1 Model Inverse and Joint Variation

The Equation of Direct Variation The equation y = ax represents direct variation between x and y y is said to vary directly with x. Constant of Variation The nonzero constant a is called the constant of variation. (Basically, a is slope)

Important: For a relation to be considered a direct variation, THE RELATION MUST BE LINEAR AND PASS THROUGH THE ORIGIN (0, 0)

Inverse Variation Two Variables x and y show inverse variation if they are related as follows:

Before classifying equations: SOLVE FOR Y!

Classify as direct variation, inverse variation, or neither.

Write an inverse variation equation. Step 1: write the general equation for inverse variation. Step 2: substitute in the values. Step 3: solve for a. Step 4 Write the equation.

The variables x and y vary inversely, and y = 7 when x =4 The variables x and y vary inversely, and y = 7 when x =4. Write an equation that relates x and y. Then find y when x = -2.

The variables x and y vary inversely, and y = 3 when x = 4 The variables x and y vary inversely, and y = 3 when x = 4. Write an equation that relates x and y. Then find y when x = 2.

The variables x and y vary inversely, and y = -1 when x = 8 The variables x and y vary inversely, and y = -1 when x = 8. Write an equation that relates x and y. Then find y when x = 2.

The variables x and y vary inversely, and y = 12 when x =. 5 The variables x and y vary inversely, and y = 12 when x = .5. Write an equation that relates x and y. Then find y when x = 2.

Joint variation: Occurs when a quantity varies directly with the product of two or more other quantities. Examples: (z varies jointly with x and y.) (p varies jointly with q, r, and s.)

Write a joint variation equation. Step 1: write a general joint variation equation. Step 2: use the given values to find a. Step 3: write the equation with a. Step 4: substitute to find the missing variable.

The variable z varies jointly with x and y The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5. Write an equation that relates x, y, and z. Then find z when x = 2 and y = 6.

The variable z varies jointly with x and y The variable z varies jointly with x and y. Also, z = 7 when x = 1 and y = 2. Write an equation that relates x, y, and z. Then find z when x = -2 and y = 5.

The variable z varies jointly with x and y The variable z varies jointly with x and y. Also, z = 24 when x = 4 and y = -3. Write an equation that relates x, y, and z. Then find z when x = -2 and y = 5.

Homework: P 469 19-32, 40-45