demarcus is organizing a group of friends to attend a concert. the ticket pricing is shown in the table below. use the information to create a graph and answer the questions.

# of tickets | total cost ($)
2 | 32
3 | 48
5 | 80
7 | 112

1. rate of change: y = 16x
equation: ______

2. what does the ordered pair (1, 16) represent in this situation?

3. describe how you know that this is a proportional relationship.

4. the number of feet in a yard can be represented by a graph. circle the graph(s) that could... (graph grid shown)

(additional partial text: \your understanding of proportional relationships to answer the questions below.\ and
ships: graphs\)

Question

demarcus is organizing a group of friends to attend a concert. the ticket pricing is shown in the table below. use the information to create a graph and answer the questions.

# of tickets | total cost ($)
2 | 32
3 | 48
5 | 80
7 | 112

1. rate of change: y = 16x
equation: ______

2. what does the ordered pair (1, 16) represent in this situation?

3. describe how you know that this is a proportional relationship.

4. the number of feet in a yard can be represented by a graph. circle the graph(s) that could... (graph grid shown)

(additional partial text: \your understanding of proportional relationships to answer the questions below.\ and
ships: graphs\)

Accepted Answer

### Question 1: Rate of Change and Equation
# Explanation:
## Step 1: Calculate Rate of Change
To find the rate of change (slope) for a proportional relationship, we use the formula $ \text{Rate of Change} = \frac{\text{Change in } y}{\text{Change in } x} $. Using the first two points $(2, 32)$ and $(3, 48)$:
$ \text{Rate of Change} = \frac{48 - 32}{3 - 2} = \frac{16}{1} = 16 $
## Step 2: Determine the Equation
For a proportional relationship, the equation is of the form $ y = kx $, where $ k $ is the rate of change. Since $ k = 16 $, the equation is $ y = 16x $.
# Answer:
Rate of Change: $ 16 $
Equation: $ y = 16x $

### Question 2: Meaning of Ordered Pair $(1, 16)$
# Brief Explanations:
In the context of ticket pricing, $ x $ represents the number of tickets and $ y $ represents the total cost. The ordered pair $(1, 16)$ means that when the number of tickets ($ x $) is 1, the total cost ($ y $) is $16. So, it represents the cost of 1 ticket.
# Answer:
The ordered pair $(1, 16)$ represents that 1 ticket costs $16.

### Question 3: How to Know It's Proportional
# Brief Explanations:
A relationship is proportional if the ratio of $ y $ to $ x $ (total cost to number of tickets) is constant for all pairs of values. Let's check the ratios:
- For $(2, 32)$: $ \frac{32}{2} = 16 $
- For $(3, 48)$: $ \frac{48}{3} = 16 $
- For $(5, 80)$: $ \frac{80}{5} = 16 $
- For $(7, 112)$: $ \frac{112}{7} = 16 $
Since the ratio $ \frac{y}{x} $ is constant (16) for all data points, and the equation is $ y = 16x $ (passes through the origin $(0,0)$ as $ 0 = 16 \times 0 $), this is a proportional relationship.
# Answer:
The relationship is proportional because the ratio of total cost to number of tickets ($ \frac{y}{x} $) is constant (16) for all data points, and the equation $ y = 16x $ is a proportional equation (passes through the origin).

### Question 4: (Assuming it's about feet in a yard, 3 feet = 1 yard)
# Explanation:
## Step 1: Recall the Conversion
We know that 1 yard is equal to 3 feet. So the relationship between yards ($ x $) and feet ($ y $) is $ y = 3x $, which is a proportional relationship (passes through the origin, constant ratio $ \frac{y}{x} = 3 $).
## Step 2: Identify the Graph
A proportional relationship $ y = 3x $ is a straight line passing through the origin with a slope of 3. So we circle the graph that is a straight line through $(0,0)$ with a slope of 3 (e.g., if one graph has points like $(1, 3)$, $(2, 6)$, etc., that's the one).
# Answer:
The number of feet in a yard is a proportional relationship $ y = 3x $ (where $ x $ is yards, $ y $ is feet). Circle the graph that is a straight line through the origin with a slope of 3 (e.g., passing through $(0,0)$, $(1, 3)$, $(2, 6)$, etc.).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

of tickets | total cost ($)

Explanation:

Question 1: Rate of Change and Equation

Step 1: Calculate Rate of Change

Step 2: Determine the Equation

Answer:

Question 2: Meaning of Ordered Pair \((1, 16)\)