Question

1. fill in the blanks using the available answer choices.

a bicycle rental company charges a one time rental fee plus an hourly rate depending on how long the bike is rented. the table shows the cost of renting a bicycle for different lengths of time.

time (h), x	total cost ($), y
1	11
2	17
3	23
4	29

find and interpret the rate of change.
the rate of change is \underline{(blank 1)}, so the hourly rate is $\underline{(blank 2)}$ to rent a bicycle.

find and interpret the initial value.
the initial value is \underline{(blank 3)}, so the one time fee is $\underline{(blank 4)}$.

write the equation in the form $y = mx + b$.

$y = \underline{(blank 5)}x + \underline{(blank 6)}$

blank 1 options

• 3
• 4
• 6

blank 2 options

• 3.00
• 4.00
• 6.00

blank 3 options

• 4
• 5
• 6

blank 4 options

• 4.00
• 5.00
• 6.00

blank 5 options

• 3
• 4
• 5
• 6

blank 6 options

• 3
• 4
• 5
• 6

Explanation:

Step1: Calculate rate of change (slope)

The rate of change (slope \( m \)) is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} \). Using points \((0, 5)\) and \((1, 11)\):
\( m = \frac{11 - 5}{1 - 0} = \frac{6}{1} = 6 \).
So the rate of change is 6, and the hourly rate is $6.00.

Step2: Identify initial value (y-intercept)

The initial value is the \( y \)-value when \( x = 0 \). From the table, when \( x = 0 \), \( y = 5 \). So the initial value is 5, and the one - time fee is $5.00.

Step3: Write the equation \( y = mx + b \)

We know \( m = 6 \) (from Step 1) and \( b = 5 \) (from Step 2). So the equation is \( y = 6x + 5 \).

Answer:

Blank 1: 6
Blank 2: 6.00
Blank 3: 5
Blank 4: 5.00
Blank 5: 6
Blank 6: 5

(For each blank:
Blank 1: 6 (from the rate of change calculation).
Blank 2: 6.00 (matches the rate of change as hourly rate).
Blank 3: 5 (initial value from \( x = 0 \) in the table).
Blank 4: 5.00 (one - time fee from initial value).
Blank 5: 6 (slope \( m \) in \( y=mx + b \)).
Blank 6: 5 (y - intercept \( b \) in \( y=mx + b \)).)