Question

b. use the equation you found to complete the table.

texts	25	50	100

1. a photographer charges $150 for a sitting fee. digital images cost $15 each.

a. write a linear model that gives the total cost in dollars in terms of how many digital images you purchase.

b. use the equation to complete the table.

digital images	0	2	4	6	10

1. a car rental company charges a $75 rental fee and an additional $0.15 per mile.

a. write an equation to model the total charge in terms of the number of miles driven.

b. find the cost of renting a car for 50 miles.

c. find the number of miles you can drive if you have $135 to spend.

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Explanation:

Problem 17a:

Step1: Define variables

Let \( x \) be the number of digital images, \( y \) be total cost.

Step2: Identify slope and intercept

Sitting fee (\( y \)-intercept) \( b = 150 \), cost per image (slope) \( m = 15 \).

Step3: Write linear model

Using \( y = mx + b \), we get \( y = 15x + 150 \).

Step1: For \( x = 0 \)

Substitute \( x = 0 \) into \( y = 15x + 150 \): \( y = 15(0) + 150 = 150 \).

Step2: For \( x = 2 \)

Substitute \( x = 2 \): \( y = 15(2) + 150 = 30 + 150 = 180 \).

Step3: For \( x = 4 \)

Substitute \( x = 4 \): \( y = 15(4) + 150 = 60 + 150 = 210 \).

Step4: For \( x = 6 \)

Substitute \( x = 6 \): \( y = 15(6) + 150 = 90 + 150 = 240 \).

Step5: For \( x = 10 \)

Substitute \( x = 10 \): \( y = 15(10) + 150 = 150 + 150 = 300 \) (note: original table had 200 which is incorrect, correct is 300).

Step1: Define variables

Let \( x \) be miles driven, \( y \) be total charge.

Step2: Identify slope and intercept

Rental fee (\( y \)-intercept) \( b = 75 \), cost per mile (slope) \( m = 0.15 \).

Step3: Write equation

Using \( y = mx + b \), we get \( y = 0.15x + 75 \).

Answer:

\( y = 15x + 150 \) (where \( x \) is number of digital images, \( y \) is total cost in dollars)

Problem 17b: