John likes to solve puzzles printed in the local newspaper. He came across the following sequence in the newspaper the other day: Term 1 Term 2 Term 3

Slide 3:

7 8 9 10

Slide 4:

Term Number of Blocks

Slide 5:

FUNCTION? YES or NO LINEAR? YES or NO

Slide 6:

INDEPENDENT VARIABLE Term DEPENDENT VARIABLE Number of Blocks

Slide 7:

DOMAIN {1, 2, 3, 4,…} RANGE {6, 7, 8, 9, 10,…} 1 2 3 4 5 6 7 2 4 6 8 10 12 14 (left to right) (down to up) Data is discrete; therefore, list the domain and range.

Slide 8:

EQUATION (that fits) y = 1x + 6 INTERPRET THE EQUATION The number of blocks is equal to the term plus 6. STAT
ENTER
L1
L2
STAT
CALC
4
ENTER
ENTER

Slide 9:

SLOPE Positive 1 INTERPRET THE SLOPE The slope is increasing; 1 block per term.

Slide 10:

Determine how many blocks are in the 10th term. y = 1x + 6 y = 1(10) + 6 y = 16

Slide 11:

What term in the sequence has 36 blocks? y = 1x + 6 36 = 1x + 6 - 6 30 = 1x - 6 30 = x

Slide 12:

April is trying to lose some weight. She learned from her doctor that she can burn calories while sleeping. If she sleeps 5 hours she can burn 250 calories. If April sleeps 7 hours she can burn 400 calories and if she sleeps 9 hours she can burn 550 calories.

Slide 13:

400 550 700 250

Slide 14:

Time (hours) Calories Burned 1 2 3 4 5 6 7 100 200 300 400 500 600 700 8 9 10 11 The domain is continuous; therefore, we model with a solid line.

Slide 15:

FUNCTION? YES or NO LINEAR? YES or NO

Slide 16:

INDEPENDENT VARIABLE Time DEPENDENT VARIABLE Calories Burned

Slide 17:

DOMAIN RANGE 1.5 ≤ x ≤ ∞ OR 0 ≤ y which is the same as y > 0 (left to right) (down to up) 1.5<x which is the same as x > 1.5 OR 0 ≤ y ≤ ∞

Slide 18:

EQUATION y = 75x + -125 INTERPRET THE EQUATION The calories burned is equal to 75 times the number of hours plus -125. STAT
ENTER
L1
L2
STAT
CALC
4
ENTER
ENTER

Slide 19:

SLOPE Positive 75 INTERPRET THE SLOPE Burn 75 calories per hour

Slide 20:

Determine the total amount of calories April can burn if she sleeps for 11 hours. y = 75x + -125 y = 75(11) + -125 y = 700

Slide 21:

Determine how many hours April slept if she burned about 1000 calories. y = 75x + -125 1000 = 75x + -125 15 hours of sleep

Slide 22:

Sue lives in the US and likes to call her grandmother who lives in Canada. Sue is charged $0.50 to connect and $0.10 for every minute after. Sue talked to her grandmother for 5 minutes and was charged $1.00.

DOMAIN 0, 1, 2, 3, 4, 5, …∞ RANGE 0.50, 1.00, 1.50, 2.00,…∞ OR 0 ≤ x OR 0.50 ≤ y (left to right) (down to up)

Slide 28:

EQUATION y = 0.10x + 0.50 INTERPRET THE EQUATION The cost is equal to 0.10 times the number of minutes plus 0.50. STAT
ENTER
L1
L2
STAT
CALC
4
ENTER
ENTER

Slide 29:

SLOPE Positive 0.10 INTERPRET THE SLOPE The cost is increasing $0.10 per minute

Slide 30:

Determine the total amount of Sue will pay if talks on the phone for 1 hour. (60 minutes) y = 0.10x + 0.50 y = 0.10(60) + 0.50 y = $6.50

Slide 31:

Determine how many minutes Sue was talking on the phone if she paid $30.50. y = 0.10x + 0.50 300 minutes 30.50 = 0.10x + 0.50

Slide 32:

John wanted to clean his fish tank. First John needed to drain the tank’s water. John’s tank has 100 ml of water in it. He noticed that after 1 minute the tank had 90 ml left in it. After 2 minutes the tank had 80 ml left in it. After 3 minutes the tank had 70 ml left in it and after 4 minutes the tank had 60 ml left in it.

INDEPENDENT VARIABLE Time DEPENDENT VARIABLE Water remaining

Slide 37:

DOMAIN 0, 1, 2, 3, 4,…10 RANGE 0, 60, 70, 80, 90, 100 OR 0 ≤ x ≤ 10 OR 0 ≤ y ≤ 100 (left to right) (down to up)

Slide 38:

EQUATION y = -10x + 100 INTERPRET THE EQUATION The water remaining is equal to -10 times the number of minutes plus 100. STAT
ENTER
L1
L2
STAT
CALC
4
ENTER
ENTER

Slide 39:

SLOPE Negative 10 INTERPRET THE SLOPE Water is decreasing
10 ml per minute

Slide 40:

Determine the total amount of water left in the tank after 6 minutes. y = -10x + 100 y = -10(6) + 100 y = 40 ml of water

Slide 41:

Determine how much time it will take John to completely drain his fish tank. y = -10x + 100 10 minutes 100 = -10x + 100

Slide 42:

John likes to solve puzzles printed in the local newspaper. He came across the following sequence in the newspaper the other day:
11, 6, 1, -4, …

Slide 43:

6 1 -4 11

Slide 44:

Term Number 1 2 3 4 5 6 7 1 8 9 10 2 3 4 5 -1 -2 -3

Slide 45:

FUNCTION? YES or NO LINEAR? YES or NO

Slide 46:

INDEPENDENT VARIABLE Term DEPENDENT VARIABLE Number in the sequence

Slide 47:

DOMAIN …, 1, 2, 3, 4,… RANGE …., -4, 1, 6, 11, …. OR x is all real numbers OR y is all real numbers (left to right) (down to up)

Slide 48:

EQUATION y = -5x + 16 INTERPRET THE EQUATION The number in the sequence is equal to -5 times the term plus 16. STAT
ENTER
L1
L2
STAT
CALC
4
ENTER
ENTER

Slide 49:

SLOPE Negative 5 INTERPRET THE SLOPE The sequence is decreasing 5 units per term

Slide 50:

Determine the 10th term in the sequence. y = -5x + 16 y = -5(10) + 16 y = -34

Slide 51:

-14 is what term in the sequence? y = -5x + 16 6th term -14 = -5x + 16

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