1. Warm Up #4

2. HW Check – Inverse Worksheet

3. 2.3 - Direct Variation

4. Direct Variation
A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation.

5. Constant of Variation
The Slope, k, is constant. It can be represented at the ratio of

6. Identifying Direct Variation from a Table
Determine whether y varies directly with x. If so, find the constant of variation and write the equations X Y 2 8 3 12 5 20 X Y 1 4 2 7 5 16

7. You Try!!
Determine whether y varies directly with x. If so, find the constant of variation and write the equations X Y -1 -2 3 4 6 7 X Y -6 -2 3 1 12 4

8. Identifying Direct Variation from an Equation
For each function, determine whether y varies directly with x. If so, find the constant of variation:
y = 4x
2y = 3x
y = 2x + 3

9. You Try!!
Determine whether y varies directly with x. If so, find the constant of variation.
y = x/2
2y – 1 = x
4x = 8y
7x + 4y = 10

10. Using Proportions
If we know that y varies directly with x. We can use proportions to find missing information. Ex. Suppose y varies directly with x, and x = 3 when y = 7. Find x when y = 21.

11. You Try! y varies directly with x:
If y = 25 when x = 15, find x when y = 10
If y = 30 when x = -3, find y when x = -9

12. Writing Equations
Write an equation of the direct variation that includes the point (10, -15). You Try: Write an equation of the direct variation that includes the point (-40, 16).

13. Word Problems
The Height of an object varies directly with the length of its shadow. A person 6 ft tall casts an 8.5 ft shadow, while a tree casts a 38 ft shadow. How tall is the tree?

14. Word Problem
The amount of a persons paycheck p varies directly with the numbers of hours worked t. For 4o hours of work, the paycheck is $390. Write an equation for the relationship between hours worked and pay.

15. Direct Variation Worksheet Turn in when you are done!
Class work – Group Work
Direct Variation Worksheet Turn in when you are done!

16. Mid-Chapter Review Sheet # 4 – 15 Show all work for credit!!
Homework
Mid-Chapter Review Sheet # 4 – 15 Show all work for credit!!