2.2 independent practice
teks 7.4.a, 7.4.c, 7.4.d
information on three car - rental companies is given.
5. write an equation that gives the cost y of renting a car for x days from rent - all.
6. what is the cost per day of renting a car from a - 1?
7. analyze relationships which company offers the best deal? why?
8. critique reasoning a skydiver jumps out of an airplane. after 0.8 second, she has fallen 100 feet. after 3.1 seconds, she has fallen 500 feet. emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. is his answer reasonable? explain.
steven earns extra money babysitting. he charges $31.25 for 5 hours and $50 for 8 hours.
9. explain why the relationship between how much steven charges and time is a proportional relationship.
10. interpret the answer explain what the constant rate of change means in the context.
11. write an equation to represent the relationship. tell what the variables represent.
12. how much would steven charge for 3 hours?

Question

Accepted Answer

### 5.
# Explanation:
## Step1: Find the daily - rate for Rent - All
First, find the difference in cost and days. For Rent - All, when the number of days changes from 3 to 4 (a change of $\Delta x=4 - 3=1$ day), the cost changes from $55.50$ to $74.00$ (a change of $\Delta y=74.00 - 55.50 = 18.5$). The daily rate (slope $m$) is $\frac{\Delta y}{\Delta x}=18.5$. Since the relationship is linear and when $x = 0$, $y = 0$ (no days, no cost), the equation is $y=18.5x$.
# Answer:
$y = 18.5x$

### 6.
# Explanation:
## Step1: Calculate the daily - rate for A - 1 Rentals
For A - 1 Rentals, the cost $y$ of renting a car for $x$ days is $10.99$ for each half - day. Since there are 2 half - days in a day, the cost per day is $10.99	imes2=21.98$.
# Answer:
$\$21.98$

### 7.
# Explanation:
## Step1: Compare the daily rates
Rent - All has a daily rate of $18.5$ dollars per day, A - 1 Rentals has a daily rate of $21.98$ dollars per day, and Car Town has a daily rate of $19.25$ dollars per day. Since $18.5<19.25<21.98$, Rent - All offers the best deal because it has the lowest daily rental cost.
# Answer:
Rent - All offers the best deal because it has the lowest daily rental cost.

### 8.
# Explanation:
## Step1: Assume a linear relationship (for simplicity)
Let's assume a linear relationship between time $t$ and distance $d$ fallen. We have two points $(t_1,d_1)=(0.8,100)$ and $(t_2,d_2)=(3.1,500)$. The slope $m$ of the line is $m=\frac{d_2 - d_1}{t_2 - t_1}=\frac{500 - 100}{3.1 - 0.8}=\frac{400}{2.3}\approx173.91$. The equation of the line in point - slope form is $d - 100=173.91(t - 0.8)$. When $t = 1.5$, $d-100=173.91	imes(1.5 - 0.8)=173.91	imes0.7 = 121.737$, so $d=100 + 121.737=221.737$. Since $187.5$ is close to the value calculated assuming linear - fall (but in reality, free - fall is a non - linear motion due to air resistance), his answer is somewhat reasonable if we consider a simple linear approximation.
# Answer:
His answer is somewhat reasonable if we consider a simple linear approximation of the skydiver's fall, but in reality, free - fall is non - linear due to air resistance.

### 9.
# Explanation:
## Step1: Calculate the rate of change
For Steven's babysitting, the rate of change (unit rate) for the first case is $\frac{31.25}{5}=6.25$ dollars per hour, and for the second case is $\frac{50}{8}=6.25$ dollars per hour. Since the ratio of the amount he charges to the number of hours worked is constant ($6.25$), the relationship is proportional.
# Answer:
The ratio of the amount Steven charges to the number of hours worked is constant ($6.25$ dollars per hour), so the relationship is proportional.

### 10.
# Explanation:
## Step1: Interpret the constant rate of change
The constant rate of change of $6.25$ means that Steven charges $6.25$ dollars for each additional hour of babysitting. It represents his hourly rate.
# Answer:
The constant rate of change of $6.25$ represents Steven's hourly babysitting rate.

### 11.
# Explanation:
## Step1: Write the proportional equation
Let $y$ be the amount Steven charges and $x$ be the number of hours he babysits. Since the relationship is proportional with a constant of proportionality (rate) $k = 6.25$, the equation is $y=6.25x$, where $y$ is the total amount charged and $x$ is the number of hours of babysitting.
# Answer:
$y = 6.25x$, where $y$ is the total amount Steven charges for babysitting and $x$ is the number of hours of babysitting.

### 12.
# Explanation:
## Step1: Use the equation to find the charge
We use the equation $y = 6.25x$. When $x = 3$, $y=6.25	imes3=18.75$.
# Answer:
$\$18.75$

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QUESTION IMAGE

Question

Explanation:

5.

Step1: Find the daily - rate for Rent - All

Step1: Calculate the daily - rate for A - 1 Rentals

Step1: Compare the daily rates

Answer:

6.