1. {(-2, 3), (-1, 2), (0, 2), (-2, 9)}a. Is it a function? Explain.b. What is the domain?c. What is the range?

2. Bowling costs $4.50 per game. Shoe rental costs $3.75. Write a function that models the total cost of games and shoe rental. Evaluate the function for 10 games.

Warm – up #1

1. {(-2, 3), (-1, 2), (0, 2), (-2, 9)}a. Is not a function. When x =-2, there are TWO y values.

b. Domain: {-2, -1, 0}

c. Range: {2, 3, 9}

Warm – up #1 Solutions

2.

For 10 games

Warm – up #1 Solutions

Homework Log

Tues

9/22

Lesson 2 – 2

Learning Objective: To write & interpret direction variation eq’ns

Hw: Pg. 71 #7, 9, 19 – 25 odd, 39 – 45 odd, CC*51, 52, 71

9/22/15 Lesson 2-2 Direct Variation

Algebra II

To write & interpret direct variation equations

Learning Objective

Direct Variation – If input (x) increase, then output (y) increase. If input (x) decrease, then output (y) decreases.

y = kx

Constant of variation k – the ratio of ALL output-input pairs equal k

1. Determine whether y varies directly with x.

Yes, y varies directly with x.

The constant of variationk is 2.

y = kx y = 2x

Identifying Direct Variation

2. Determine whether y varies directly with x.

No, y does not vary directly with x.

is not constant

Identifying Direct Variation

In a direct variation, is the same for all pairs of data, so you can solve a direct variation by a proportion

Solving Direct Variation

3. Suppose y varies directly with x, and y = 9, when x = -15. What is y when x = 21.

-15y = 9(21)-15y = 189-15 -15

y =-12.6

Solving Direct Variation

4. Suppose y varies directly with x, and y = 15, when x = 3. What is x when y = 60.

15x = 3(60)15x = 18015 15

x =12

Solving Direct Variation

5. Write a direct variation equation that passes through (3, -15)

y = kx-15 = k(3) 3 3-5 = k

y = -5x

Writing a Direct Variation

6. Write a direct variation equation that passes through (-7, -5)

y = kx-5 = k(-7)-7 -7 = k

y =

Writing a Direct Variation

7. A salesperson’s commission varies directly with sales. For $1000 in sales, the commission is $85. What is the commission for $2300 in sales?y= commission x = sales

1000y = 85(2300)1000y = 1955001000 1000

y = $195.50

Solving Direct Variation

8. The number of calories varies directly with the mass of cheese. If 50 grams of cheese contains 200 calories, how many calories are in 70 grams of cheese?y= calories x = cheese

50y = 200(70)50y = 1400050 50y = 280 calories

Solving Direct Variation

Slope ReviewAlgebra II

1. (-3, 7) & (-2, 4)

Find parallel slope-3

Find perpendicular slope

Find Slope

2. (3, 1) & (-4, 1)

horizontal line!

At y = 1

Find Slope

3. (7, 3) & (7, 1)

vertical line!at x = 7

Find Slope

CANNOT DIVIDE BY ZERO!!

When slope is undefined, the graph is a vertical line.

Parallel line would also be vertical with a slope that is undefined.

Perpendicular line would be horizontal with a slope that is 0.

Perpendicular & Parallel Slope

When slope is 0, the graph is a horizontal line.

Parallel line would also be horizontal with a slope of 0.

Perpendicular line would be vertical with a slope that is undefined.

Perpendicular & Parallel Slope

Explain why you cannot answer the following question.

If y = 0 when x = 0, what is x when y = 13?

Ticket Out the Door

Assignment:

Pg. 71 #7, 9, 19 – 25 odd, 39 – 45 odd, CC*51, 52, 71