1. Direct, Inverse & Joint Variation Section 2.5

2. Direct Variation 2 variables X & Y show direct variation provided y = kx & k ≠ 0. The constant k is called the constant of variation, & y is said to vary directly with x. The graph of y = kx is a line through the origin.

3. The variables x & y vary directly, & y = 12 when x = 4. Write and graph an equation relating x & y. Use x & y to find the constant of variation y = kx 12 = k4 3 = k The direct variation equation is y = 3x This is what you MUST write as the answer!

4. In the same direct variation equation, when x=5, find the value of y. y = 3*5 y = 15

5. Summary… Direct Variation Use y=kx. varies directly Means “y varies directly with x.” constant of variation k is called the constant of variation.

6. New stuff! Inverse Variation varies inversely “y varies inversely with x.” constant of variation k is the constant of variation.

7. Ex: tell whether x & y show direct variation, inverse variation, or neither. a.xy=4.8 b.y=x+4 c. Hint: Solve the equation for y and take notice of the relationship. Inverse Variation Neither Direct Variation

8. Ex: The variables x & y vary inversely, and y=8 when x=3. Write an equation that relates x & y. k=24 Find y when x= -4. y= -6

9. Assignment Page 224 Problems 2 – 12 evens

10. Joint Variation When a quantity varies directly as the product of 2 or more other quantities. For example: if z varies jointly with x & y, then z=kxy. Ex: if y varies inversely with the square of x, then y=k/x 2. Ex: if z varies directly with y and inversely with x, then z=ky/x.

11. Examples: Write an equation. y varies directly with x and inversely with z 2. y varies inversely with x 3. y varies directly with x 2 and inversely with z. z varies jointly with x 2 and y. y varies inversely with x and z.

12. Assignment P. Problems