Student Page 2.7.5 Slope and \(y\)-Intercept in Context
1.
For each story:
Create a table.
Plot the data in the table electronically.
Find the slope and \(y\)-intercept. Explain how you know each is correct based on the context.
Determine an equation.
Graph the equation electronically on the same graph as in Item 2.7.5.1.b to verify the equation fits the data.
(a)
At a comedy club, the entrance fee is $15. Beverages cost $5 each. How much will you pay overall including entrance fee and \(x\) beverages?
(i) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(ii) Equation.
Answer:
(iii) Slope.
How do you know you're right?
(iv) Intercept.
How do you know you're right?
(b)
Charity always leaves a generous tip when she eats out. She leaves a 15% tip plus $2 regardless of the amount of the bill. How much tip will she leave based on the amount of the bill?
(i) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(ii) Equation.
Answer:
(iii) Slope.
How do you know you're right?
(iv) Intercept.
How do you know you're right?
(c)
Alan really likes apples. He pays $1.25 for each apple he buys at the Commons. He has a food card with $50 on it that he only uses to purchase apples. What is the amount, \(y\text{,}\) available on the card after purchasing \(x\) apples?
(i) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(ii) Equation.
Answer:
(iii) Slope.
How do you know you're right?
(iv) Intercept.
How do you know you're right?
(d)
To park in a downtown parking lot, you pay $60 for a sticker giving you the privilege of parking in the lot. The daily charge (once you have the sticker) is $5/day. How much have you paid to park in the lot after \(x\) days?
(i) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(ii) Equation.
Answer:
(iii) Slope.
How do you know you're right?
(iv) Intercept.
How do you know you're right?
(e)
Barnes and Noble charges $25 for a yearly membership. B&N members get a 20% discount on every purchase. How much will a member pay per year if she buys \(x\) dollars worth of books at Barnes and Noble?
(i) Table.
| \(x\) | \(y\) |
|---|---|
| 100 | |
| 200 | |
| 300 | |
| 400 | |
| 500 | |
| 600 | |
| \(x\) |
(ii) Equation.
Answer:
(iii) Slope.
How do you know you're right?
(iv) Intercept.
How do you know you're right?
(f)
Daevon plays basketball at the Y. The Y charges $52 each month plus a $20 initiation fee. How much will Daevon pay for \(x\) months of use of the Y?
(i) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(ii) Equation.
Answer:
(iii) Slope.
How do you know you're right?
(iv) Intercept.
How do you know you're right?
2.
Create two different stories that relate to your life. One story must have a negative slope. The other must have a positive slope. Fill-in the following for your stories.
(a)
(i) Story.
Answer:
(ii) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(iii) Equation.
Answer:
(iv) Slope.
Answer:
(v) Intercept.
Answer:
(vi) Story.
Answer:
(vii) Table.
| \(x\) | \(y\) |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| \(x\) |
(viii) Equation.
Answer:
(ix) Slope.
Answer:
(x) Intercept.
Answer: