Math 9 Linear Relations Assignment PDF

## MATH 9 ### Linear Relations #### Interpolating and Extrapolating Data Points **Assignment** 1. This graph represents a linear relation, determine the following. | x | y | |---|---| | -3 | -4 | | 6 | 5 | | -1 | -2 | | 3 | 2 | | 2 | 1 | | 4 | 3 | 2. This graph shows the area, A square meters,...

## MATH 9 ### Linear Relations #### Interpolating and Extrapolating Data Points **Assignment** 1. This graph represents a linear relation, determine the following. | x | y | |---|---| | -3 | -4 | | 6 | 5 | | -1 | -2 | | 3 | 2 | | 2 | 1 | | 4 | 3 | 2. This graph shows the area, A square meters, that paint covers related to its volume, V liters. * **a)** What area is covered by 6 L of paint? 54m² * **b)** What volume of paint would cover 45 m²? 5L * **c)** This relation is **direct** or **partial** (circle the correct answer). - goes through origin (0,0) 3. This graph shows the cost for a house call by an electrician for up to 6 hours of work. * **a)** The electrician charges $180 to complete a job. For how many hours did she work? 3h * **b)** If the job cost $240, how long did the electrician work? 4.2-4.3h * **c)** What was the cost of just the service call? $60 - (y-intercept) - zero hours worked * **d)** This relation is **direct** or **partial** (circle the correct answer). 4. This graph shows the distance, d meters, travelled by Jadan on her bicycle related to the number of wheel revolutions, n, as she rode from Whitehorse to the Grey Mountains. * **a)** How far was Jada from the Grey Mountains when she started her bicycle trip? 6000m * **b)** This relation is **direct** or **partial** (circle the correct answer). 5. This graph represents Eric's snowmobile ride. * **a)** How far was Eric from home after he had travelled 2 ¼ hours? 64-66 km * **b)** How long did it take Eric to travel 45 km from home? 1.3-1.4h * **c)** How far from his home did Eric start his ride? 10km - zero time, y-intercept. (t=0) 6. This graph shows the height of a candle related to the time it has been burning. * **a)** How tall was the candle prior to it being lit? 10cm zero time (t=0) * **b)** How long did it take to burn out? 45min * **c)** At what rate was it burning (cm/min)? -2/9=0.22cm/min * rate of burning = slope M=Ah-ha-hi-0-10 / Ot tz-t, 45-0 7. The graph shows the recommended maximum heart rate of a person, R beats/min, related to their age, a years, for a stress test. * **a)** Why is there not an R-intercept? -Not born yet. * **b)** At what age is the recommended maximum heart rate 120 beats/minute? 76-78 years * **c)** What is the approximate recommended heart rate for a person aged 70? 125-127 beats/min 8. This graph shows the cost of a cab, C dollars, related to the distance travelled, d kilometers. * **a)** What is the cost when the distance is 7 km? $14 * **b)** What is the distance when the cost is $9.50? 3.8-3.9km 9. Northlands School Outdoor Club had a fundraiser to help purchase snowshoes. The club had 300 power bars to sell. This graph shows the profit made from selling the power bars. * ** a)** How many power bars have to be sold before the school begins to make a profit? 50 * **b)** What is the setup cost for the fundraiser? $40 (y-intercept) - zero bars sold * **c)** What is the profit if the following number of power bars are sold? * i) 200 $120 * ii) 275 $180 * **b)** How many power bars have to be sold to make each profit? * i) $80 150 bars * ii) $140 225 bars 10. The capacity of each two fuel tanks is 100 m³. * **a)** Does it take longer to fill an empty tank or to empty it? Fill rate (A) M=V=V2-V St ta-t, M=100-0 50-0. M=1002m/min Empty Rate (B) N=AVV-V St Ez-ti M=0-100 25-0 = -100 = -4m³/min * **b)** After 10 minutes, how much fuel has been filled into the tank? 20 m³ * **c)** After 10 minutes, how much fuel has been emptied from the tank? 40 m³ 11. Which graph has a rate of change of -5 and a vertical intercept of 100? Graph A 12. The graph shows the relationship between air pressure, in kilopascals, and altitude, in meters. * **a)** What is the approximate air pressure at an altitude of 1500 m? 82-83 kPa of 2400 m? 70-72 kPa * **b)** Approximately at what altitude is the air pressure 90 kPa? 1000m 60 kPa? 3000~ 13. The table of shows the relationship between stopping distance and speed of vehicle. Plot the linear relation on a graph. | Speed, s (km/h) | Stopping Distance, d (m) | |---|---| | 0 | 0 | | 15 | 10 | | 30 | 20 | | 45 | 30 | | 60 | 40 | | 80 | 53 | | 37.5 | 25 | * **a)** Determine the approximate stopping distance for a speed of 80 km/h * **b)** Determine the approximate speed for a vehicle that took25 m to stop - m=ad/gs=gs= - d=gs/3 - (a) d= 4/3 (80) ≈ 53m - (b) 25=2/3s ≈ 37.5km/h