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Slope in context

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DawnWagner15

Finding Slope from Word Problems. This was made for an Adult Education class studying for their high school equivalency

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SLOPE IN CONTEXT Independent and Dependent Variables
REVIEW Calculate slope of a line that contains these two points 1. (4, 10) (7, 12) 2. (2, 5) (1, 3) 3. (0, 6) (-1, 8)
Slope in context
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? Slope in context: (x,y) X is input or independent variable (Time is independent because it happens regardless) y is output or dependent variable ( altitude is dependent on how many hours the climber is climbing)
Lets practice identifying independent versus dependent variables Khan Academy: Independent versus dependent variables
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? Which is the independent and dependent variables? Which is an input and which is an output? Determine the two points from the given information. In this case time in hours is x while output y is feet. (2,400) (6, 700) Now use the points to calculate slope using slope formula x1 y1 x2 y2 2 400 6 700 700 400 6 2 300/4 = 75 feet per hour
A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change? What are the coordinate points from the information in the problem? (____,____) (_____,____) Calculate slope What is the independent variable (X)? What is the dependent variable (y)?
A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change? What are the coordinate points from the information in the problem? (10,30) (40,100) Calculate slope What is the independent variable (X)? Seconds What is the dependent variable (y)? Feet 100 30 40 10 70 30 2 1/3 feet/sec
A woman weighed 140 lbs. in 1996 and weighs 190 lbs. in 2016. What was the rate of change in weight? Which rate sounds correct? Weight per year or year per weight?? How would we write this as coordinates? (____,____) (____,____)
A teacher weighed 140 lbs. in 1996 and weighs 190 lbs. in 2016. What was the rate of change in weight? ( 1996, 140) (2016, 190) = = 2.5 lbs. per year
Slope in context
Slope in context
Try These 1. Katteren started a savings account with $300. After 5 weeks, she had $350, and after 9 weeks, she had $400. What was the rate of change of money in her savings account per week? 2. A plane left Chicago at 8:00 A.M. At 1:00 P.M. the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip? 3. After 30 baseball games, a player had 25 hits. If after 100 games he had 80 hits, what is his average hits per baseball game?
1. Katteren started a savings account with $300. After 5 weeks, she had $350, and after 9 weeks, she had $400. What was the rate of change of money in her savings account per week? $10 per week 2. A plane left Chicago at 8:00 A.M. At 1:00 P.M. the plane landed in Los Angeles, which is 1500 miles away. What was the average speed per hour of the plane for the trip? 300 miles per hour 3. After 30 baseball games, a player had 25 hits. If after 100 games he had 80 hits, what is his average hits per baseball game? 11/14 or about 0.79 hits per game
EXTRA Practice IXL Find a slope from a graph Code YH9 IXL Find the slope from two points Code VZG IXL Identify independent and dependent variables 9UJ Khan Academy: Independent versus dependent variables Khan Academy:Slope and intercept meaning in context
More word problem practice 1. A rental car company charges a base fee and an additional charge based on how many miles the car has been driven. If one client was charged $59.00 and drove 80 miles and another client was charged $83.00 and drove 160 miles, what is the cost per mile? 2. Bike rentals are available on the canal. One patron paid $26.00 for 5 hours while another patron paid $42.00 for 9 hours. What is the average rate of change? How much was the cost per hour? 3. An airplane is descending for a landing. After 3 minutes, it is at 24,000 feet above the ground. After 5 minutes, it is 20,000 feet above the ground. What is the rate of change?
4. A hairstylist has to pay each month for her booth. At 12 haircuts she breaks even, and at 27 haircuts she makes a profit of $285. How much does she charge per haircut? 5. A yoga studio charges a yearly sign up fee, and a per class charge. If Celeste spent a total of $55.00 after 6 classes and $75.00 after 10 classes. How much does the studio charge per class? 6. A reception hall charges a reservation fee and a per plate cost for each guest. It charges $147 for 6 guests and $255 for 15 guests. How much is the cost per guest?
Answers 1. (80, $59) (160,$83) 8359 16080 = $0.30 per mile 2. (5,$26) ( 9,$42) 4226 95 = $4 per hour 3. (3, 24,000) (5, 20,000) 20,00024,000 53 = -2000 feet per minute 4. (12,$0) (27, $285) 2850 2712 = $19 per haircut 5. (5, $55) (10,$75) 7555 105 = $4 per class 6. (6, $147) (15, $255) 255147 156 = $12 per plate

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Slope in context

  • 1. SLOPE IN CONTEXT Independent and Dependent Variables
  • 2. REVIEW Calculate slope of a line that contains these two points 1. (4, 10) (7, 12) 2. (2, 5) (1, 3) 3. (0, 6) (-1, 8)
  • 4. A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? Slope in context: (x,y) X is input or independent variable (Time is independent because it happens regardless) y is output or dependent variable ( altitude is dependent on how many hours the climber is climbing)
  • 5. Lets practice identifying independent versus dependent variables Khan Academy: Independent versus dependent variables
  • 6. A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? Which is the independent and dependent variables? Which is an input and which is an output? Determine the two points from the given information. In this case time in hours is x while output y is feet. (2,400) (6, 700) Now use the points to calculate slope using slope formula x1 y1 x2 y2 2 400 6 700 700 400 6 2 300/4 = 75 feet per hour
  • 7. A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change? What are the coordinate points from the information in the problem? (____,____) (_____,____) Calculate slope What is the independent variable (X)? What is the dependent variable (y)?
  • 8. A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change? What are the coordinate points from the information in the problem? (10,30) (40,100) Calculate slope What is the independent variable (X)? Seconds What is the dependent variable (y)? Feet 100 30 40 10 70 30 2 1/3 feet/sec
  • 9. A woman weighed 140 lbs. in 1996 and weighs 190 lbs. in 2016. What was the rate of change in weight? Which rate sounds correct? Weight per year or year per weight?? How would we write this as coordinates? (____,____) (____,____)
  • 10. A teacher weighed 140 lbs. in 1996 and weighs 190 lbs. in 2016. What was the rate of change in weight? ( 1996, 140) (2016, 190) = = 2.5 lbs. per year
  • 13. Try These 1. Katteren started a savings account with $300. After 5 weeks, she had $350, and after 9 weeks, she had $400. What was the rate of change of money in her savings account per week? 2. A plane left Chicago at 8:00 A.M. At 1:00 P.M. the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip? 3. After 30 baseball games, a player had 25 hits. If after 100 games he had 80 hits, what is his average hits per baseball game?
  • 14. 1. Katteren started a savings account with $300. After 5 weeks, she had $350, and after 9 weeks, she had $400. What was the rate of change of money in her savings account per week? $10 per week 2. A plane left Chicago at 8:00 A.M. At 1:00 P.M. the plane landed in Los Angeles, which is 1500 miles away. What was the average speed per hour of the plane for the trip? 300 miles per hour 3. After 30 baseball games, a player had 25 hits. If after 100 games he had 80 hits, what is his average hits per baseball game? 11/14 or about 0.79 hits per game
  • 15. EXTRA Practice IXL Find a slope from a graph Code YH9 IXL Find the slope from two points Code VZG IXL Identify independent and dependent variables 9UJ Khan Academy: Independent versus dependent variables Khan Academy:Slope and intercept meaning in context
  • 16. More word problem practice 1. A rental car company charges a base fee and an additional charge based on how many miles the car has been driven. If one client was charged $59.00 and drove 80 miles and another client was charged $83.00 and drove 160 miles, what is the cost per mile? 2. Bike rentals are available on the canal. One patron paid $26.00 for 5 hours while another patron paid $42.00 for 9 hours. What is the average rate of change? How much was the cost per hour? 3. An airplane is descending for a landing. After 3 minutes, it is at 24,000 feet above the ground. After 5 minutes, it is 20,000 feet above the ground. What is the rate of change?
  • 17. 4. A hairstylist has to pay each month for her booth. At 12 haircuts she breaks even, and at 27 haircuts she makes a profit of $285. How much does she charge per haircut? 5. A yoga studio charges a yearly sign up fee, and a per class charge. If Celeste spent a total of $55.00 after 6 classes and $75.00 after 10 classes. How much does the studio charge per class? 6. A reception hall charges a reservation fee and a per plate cost for each guest. It charges $147 for 6 guests and $255 for 15 guests. How much is the cost per guest?
  • 18. Answers 1. (80, $59) (160,$83) 8359 16080 = $0.30 per mile 2. (5,$26) ( 9,$42) 4226 95 = $4 per hour 3. (3, 24,000) (5, 20,000) 20,00024,000 53 = -2000 feet per minute 4. (12,$0) (27, $285) 2850 2712 = $19 per haircut 5. (5, $55) (10,$75) 7555 105 = $4 per class 6. (6, $147) (15, $255) 255147 156 = $12 per plate