slopes_in_the_real_w orld

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Slopesin the Real World :

Slopesin the Real World

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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

7 8 9 10

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Term Number of Blocks

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FUNCTION? YES or NO LINEAR? YES or NO

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INDEPENDENT VARIABLE Term DEPENDENT VARIABLE Number of Blocks

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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.

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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

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

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

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

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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.

400 550 700 250

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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.

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FUNCTION? YES or NO LINEAR? YES or NO

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INDEPENDENT VARIABLE Time DEPENDENT VARIABLE Calories Burned

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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 ≤ ∞

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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

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SLOPE Positive 75 INTERPRET THE SLOPE Burn 75 calories per hour

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

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

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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.

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\$1.00 \$1.50 \$2.00 \$0.50

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Time (minutes) Cost 1 2 3 4 5 6 7 \$0.50 \$0.70 8 9 \$0.90 \$1.10

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FUNCTION? YES or NO LINEAR? YES or NO

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INDEPENDENT VARIABLE Time DEPENDENT VARIABLE Cost

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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)

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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

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

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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

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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

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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.

80 70 60 90

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Time (minutes) Water remaining (ml) 1 2 3 4 5 6 7 20 8 9 10 11 40 60 80 100 12 13 14 15

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FUNCTION? YES or NO LINEAR? YES or NO

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INDEPENDENT VARIABLE Time DEPENDENT VARIABLE Water remaining

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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)

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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

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

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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

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

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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, …

6 1 -4 11

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

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FUNCTION? YES or NO LINEAR? YES or NO

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INDEPENDENT VARIABLE Term DEPENDENT VARIABLE Number in the sequence

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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)

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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

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

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

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