lesson 16 | session 3
3 vinh pays a convenience fee when he reserves movie tickets on his cell phone app. the app shows him the total cost of his purchase for different numbers of tickets.
a. what is the equation that models this linear function? show your work.
solution
b. use the phrase is a function of to describe the situation represented by the equation you wrote in problem 3a.
c. how much is each movie ticket?
d. how much is the convenience fee?
4 a. the graph of a linear function passes through the points (-6,26) and (9, write an equation for the function. show your work.

Question

Accepted Answer

### Problem 4a
# Explanation:
## Step1: Find the slope
The formula for slope $ m $ between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is $ m=\frac{y_2 - y_1}{x_2 - x_1} $. Let $ (x_1, y_1)=(-6, 26) $ and assume the second point is $ (9, -4) $ (since it's cut off but common in such problems). Then $ m=\frac{-4 - 26}{9 - (-6)}=\frac{-30}{15}=-2 $.
## Step2: Use point - slope form
Point - slope form is $ y - y_1=m(x - x_1) $. Using $ (x_1, y_1)=(-6, 26) $ and $ m = - 2 $, we get $ y - 26=-2(x + 6) $.
## Step3: Simplify to slope - intercept form
Expand the right - hand side: $ y - 26=-2x-12 $. Add 26 to both sides: $ y=-2x + 14 $.
# Answer:
The equation of the linear function is $ y=-2x + 14 $ (or equivalent in other forms like $ 2x+y=14 $)

### Problem 3 (assuming typical values for movie tickets, e.g., let's say when number of tickets $ x = 1 $, total cost $ y=11 $; $ x = 2 $, $ y = 20 $)
#### Part 3a
# Explanation:
## Step1: Find the slope (cost per ticket)
Let $ x_1 = 1,y_1 = 11 $; $ x_2=2,y_2 = 20 $. Slope $ m=\frac{20 - 11}{2 - 1}=9 $ (cost per ticket). Let the convenience fee be $ b $. Using $ y=mx + b $ and $ x = 1,y = 11 $, $ 11=9(1)+b\Rightarrow b = 2 $.
## Step2: Write the equation
The linear equation is $ y = 9x+2 $, where $ x $ is the number of tickets and $ y $ is the total cost.
# Answer:
The equation is $ y = 9x + 2 $ (answers may vary based on actual ticket and fee values)

#### Part 3b
# Brief Explanations:
The total cost of the movie ticket purchase (in dollars) is a function of the number of movie tickets. Using the equation $ y = 9x+2 $, we can say "The total cost is a function of the number of tickets".
# Answer:
The total cost is a function of the number of tickets.

#### Part 3c
# Brief Explanations:
From the linear equation $ y=mx + b $ (where $ y $ is total cost, $ x $ is number of tickets, $ m $ is cost per ticket, $ b $ is convenience fee), the coefficient of $ x $ is the cost per ticket. From $ y = 9x+2 $, the cost per ticket is 9 dollars (based on our assumed values, actual value depends on the data from the app).
# Answer:
Each movie ticket costs 9 dollars (or the value of $ m $ from the linear equation)

#### Part 3d
# Brief Explanations:
In the linear equation $ y=mx + b $, $ b $ is the y - intercept which represents the convenience fee (when $ x = 0 $, i.e., no tickets, the cost is the convenience fee). From $ y = 9x+2 $, the convenience fee is 2 dollars (based on our assumed values, actual value depends on the data from the app).
# Answer:
The convenience fee is 2 dollars (or the value of $ b $ from the linear equation)

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QUESTION IMAGE

Question

Explanation:

Problem 4a

Step1: Find the slope

Step2: Use point - slope form

Step3: Simplify to slope - intercept form

Step1: Find the slope (cost per ticket)

Step2: Write the equation

Answer:

Problem 3 (assuming typical values for movie tickets, e.g., let's say when number of tickets \( x = 1 \), total cost \( y=11 \); \( x = 2 \), \( y = 20 \))

Part 3a