Question

slope - intercept matching

1. suppose that the water level of the russo river is 34 feet and that it is receding at a rate of 0.5 foot per day.
2. tonys father is thinking of buying his son a six - month movie pass for $40. with the pass, movies cost $1.00 each.
3. for babysitting, gia charges a flat fee of $3, plus $5 per hour.
4. saras plumbing charges $25 for a service call plus $50 per hour of service.
5. nico collected 100 pounds of aluminum cans to recycle. he plans to collect an additional 25 pounds each week.
6. rafaella canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe.
7. gigis restaurant charges $100 to rent a party room and $12 for each person for unlimited pizza and soda.
8. romano & ricci attorneys at law charge a fixed fee on $250 for an initial meeting and $100 per hour for all hours worked after that.
9. a water tank already contains 30 gallons of water when marino begins to fill it. water flows into the tank at a rate of 20 gallons per hour.
10. blue box charges a $5 membership fee and $3 for each dvd rented.
11. mrs. farini has a small business making dessert baskets. she estimates that her fixed weekly costs for rent and electricity are $250. the ingredients for one dessert basket cost $3 each.
12. angelo has to choose between two gym membership plans. plan a: $50 monthly membership fee and $10 per visit.
13. plan b costs $25 monthly one - time membership fee and $15 per visit.
14. pizza pizza pizza offers the following \deals\: deal #1: $10 for one large pizza and $5 for each additional large pizza on the same order
15. deal#2: $6.00 per large pizza

y = 25x + 100
y = 12x + 100
y = 30x + 20
y = 15x + 25
y = 5x + 3
y = 3x + 250
y = 5x + 10
y = 50x + 25
y = 50x + 10
y = 100x + 50
y = 20x + 30
y = x + 40
y = 10x + 50
y = 3x + 5
y = 6x
y = - 0.5x + 34
y = 6x + 10
y = 100x + 250

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Match problem 1

The water level of the Russo River is 34 feet and is receding at a rate of 0.5 foot per day. The equation is $y=-0.5x + 34$, which matches with the equation $y=-0.5x + 34$ in the list.

Step3: Match problem 2

Tony's father buys a six - month movie pass for $40$ and movies cost $1$ each. The equation is $y = 1x+40$ or $y=x + 40$, which matches with $y=x + 40$ in the list.

Step4: Match problem 3

Gia charges a flat fee of $3$ plus $5$ per hour for babysitting. The equation is $y = 5x+3$, which matches with $y = 5x+3$ in the list.

Step5: Match problem 4

Sara's Plumbing charges $25$ for a service call plus $50$ per hour of service. The equation is $y = 50x+25$, which matches with $y = 50x+25$ in the list.

Step6: Match problem 5

Nico collected 100 pounds of aluminum cans and plans to collect 25 more pounds each week. The equation is $y = 25x+100$, which matches with $y = 25x+100$ in the list.

Step7: Match problem 6

Raffaella Canoe Rental Service charges a $20$ transportation fee and $30$ dollars an hour to rent a canoe. The equation is $y = 30x+20$, which matches with $y = 30x+20$ in the list.

Step8: Match problem 7

Gigi's Restaurant charges $100$ to rent a party room and $12$ for each person for unlimited pizza and soda. The equation is $y = 12x+100$, which matches with $y = 12x+100$ in the list.

Step9: Match problem 8

Romano & Ricci Attorneys at Law charge a fixed fee of $250$ for an initial meeting and $100$ per hour for all hours worked after that. The equation is $y = 100x+250$, which matches with $y = 100x+250$ in the list.

Step10: Match problem 9

A water tank already contains 30 gallons of water when Marino begins to fill it. Water flows into the tank at a rate of 20 gallons per hour. The equation is $y = 20x+30$, which matches with $y = 20x+30$ in the list.

Step11: Match problem 10

Blue Box charges a $5$ membership fee and $3$ for each DVD rented. The equation is $y = 3x+5$, which matches with $y = 3x+5$ in the list.

Step12: Match problem 11

Mrs. Farini has fixed weekly costs of $250$ and ingredients cost $3$ per dessert basket. The equation is $y = 3x+250$, which matches with $y = 3x+250$ in the list.

Step13: Match problem 12

Plan A of the gym membership has a $50$ monthly membership fee and $10$ per visit. The equation is $y = 10x+50$, which matches with $y = 10x+50$ in the list.

Step14: Match problem 13

Plan B of the gym membership has a $25$ monthly one - time membership fee and $15$ per visit. The equation is $y = 15x+25$, which matches with $y = 15x+25$ in the list.

Step15: Match problem 14

Pizza Pizza Pizza's Deal #1: $10$ for one large pizza and $5$ for each additional large pizza. The equation is $y = 5x+10$, which matches with $y = 5x+10$ in the list.

Step16: Match problem 15

Pizza Pizza Pizza's Deal #2: $6$ per large pizza. The equation is $y = 6x$, which matches with $y = 6x$ in the list.

Answer:

1. $y=-0.5x + 34$
2. $y=x + 40$
3. $y = 5x+3$
4. $y = 50x+25$
5. $y = 25x+100$
6. $y = 30x+20$
7. $y = 12x+100$
8. $y = 100x+250$
9. $y = 20x+30$
10. $y = 3x+5$
11. $y = 3x+250$
12. $y = 10x+50$
13. $y = 15x+25$
14. $y = 5x+10$
15. $y = 6x$