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forget about 4 THEN >:(

7. Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of change for the function graphed to the left? 2/5, 5/4, 5/3, 5/2
Axes:

The x-axis represents "Bookmarks Sold."
The y-axis represents "Money Earned."

Data Points:

(4, 0): Indicates that selling 4 bookmarks earns $0.
(8, 10): Indicates that selling 8 bookmarks earns $10.
(12, 20): Indicates that selling 12 bookmarks earns $20.

8. Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?



Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week

First Table: Megan's Plant
Title: Megan’s Plant
Data:
Week 1: 4.5 inches
Week 2: 7 inches
Week 3: 9.5 inches
Week 4: 12 inches

Summary for Megan's Plant:
The plant height increases over the weeks.
The growth is consistent, with the height increasing by 2.5 inches from Week 1 to Week 2, 2.5 inches from Week 2 to Week 3, and 2.5 inches from Week 3 to Week 4.
This indicates a steady growth pattern.
Second Graph: Suzanne's Plant
Title: Suzanne’s Plant
Data Points:
(1, 5): At Week 1, the height is 5 inches.
(2, 7): At Week 2, the height is 7 inches.
(3, 9): At Week 3, the height is 9 inches.
(4, 11): At Week 4, the height is 11 inches.

Summary for Suzanne's Plant:
The height of the plant also increases over the weeks.
The growth appears to be consistent, with an increase of 2 inches each week.
The relationship between time (weeks) and height seems linear.

9. The graph shows the increase in temperature over time in an oven.

What is the change in the y-values and x-values on the graph?

The change in the y-values is 40 and the change in the x-values is 1.
The change in the y-values is 1 and the change in the x-values is 40.
The change in the y-values is 150 and the change in the x-values is 2.
The change in the y-values is 190 and the change in the x-values is 3.

The graph titled "Temperature Change" depicts the relationship between time (in minutes) and temperature (in Fahrenheit).

Key Observations:

Axes:

The x-axis represents time in minutes.
The y-axis represents temperature in Fahrenheit.

Data Points:

(2, 150): At 2 minutes, the temperature is 150°F.
(3, 190): At 3 minutes, the temperature is 190°F.

3 answers

Let's break down your questions one by one.

7. Rate of Change for Ellen's Bookmarks

To find the rate of change, we can use the formula:

\[ \text{Rate of Change} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{\Delta y}{\Delta x} \]

From the data points given:

  • (4, 0)
  • (8, 10)
  • (12, 20)

Using the points (8, 10) and (4, 0):

  • \(\Delta y = 10 - 0 = 10\)
  • \(\Delta x = 8 - 4 = 4\)

Now, substituting back into the formula:

\[ \text{Rate of Change} = \frac{10}{4} = \frac{5}{2} \]

So, the answer is 5/2.

8. Growth Rate of Megan's and Suzanne's Plants

  • Megan's Plant Growth:

    • From Week 1 to Week 2: \(7 - 4.5 = 2.5\) inches
    • From Week 2 to Week 3: \(9.5 - 7 = 2.5\) inches
    • From Week 3 to Week 4: \(12 - 9.5 = 2.5\) inches
    • Average Growth Rate: \(2.5\) inches per week.

  • Suzanne's Plant Growth:

    • From Week 1 to Week 2: \(7 - 5 = 2\) inches
    • From Week 2 to Week 3: \(9 - 7 = 2\) inches
    • From Week 3 to Week 4: \(11 - 9 = 2\) inches
    • Average Growth Rate: \(2\) inches per week.

Comparison:

  • Megan's plant grows at a rate of 2.5 inches per week, while Suzanne's plant grows at a rate of 2 inches per week. Thus, Megan's plant grew at a faster rate.

9. Change in Temperature Over Time

To find the change in temperature (y-values) and time (x-values) using the points given:

  • (2, 150)
  • (3, 190)

Using the points:

  • Change in y (temperature): \(190 - 150 = 40\)
  • Change in x (time): \(3 - 2 = 1\)

So, the answers are:

  • The change in the y-values (temperature) is 40.
  • The change in the x-values (time) is 1.

Thus, the correct answer is The change in the y-values is 40 and the change in the x-values is 1.

10 The graphs below show measurements from cubes with different side lengths.





Which pairs of variables have a linear relationship? Select two options.

side length and perimeter of 1 face
perimeter of 1 face and area of 1 face
surface area and volume
area of 1 face and surface area
side length and volume

Graph A: Perimeter of One Face
Title: Perimeter of 1 Face
Axes:
x-axis: Side Length
y-axis: Perimeter

Key Observations:
The data shows a positive correlation; as side length increases, the perimeter also increases.
Specific points include:
At side length 1, the perimeter is 4.
At side length 2, the perimeter is 8.
At side length 3, the perimeter is 12, and so on.

Graph B: Area of One Face
Title: Area of 1 Face
Axes:
x-axis: Perimeter
y-axis: Area

Key Observations:
The graph indicates a positive relationship between perimeter and area.
Key points include:
At a perimeter of 12, the area is 9.
At a perimeter of 20, the area is 25, suggesting that greater perimeters lead to larger areas.

Graph C: Volume vs. Surface Area
Title: Volume
Axes:
x-axis: Surface Area
y-axis: Volume

Key Observations:
There is a positive correlation; as surface area increases, volume increases too.
Specific points include:
At a surface area of 96, the volume is 64.
At a surface area of 150, the volume is 125.

Graph D: Surface Area vs. Area of One Face
Title: Surface Area
Axes:
x-axis: Area of 1 Face
y-axis: Surface Area

Key Observations:
The relationship is positive; as the area of one face increases, the surface area also increases.
Key points include:
At an area of 9, the surface area is 54.
At an area of 25, the surface area is 150.

Graph E: Volume vs. Side Length
Title: Volume
Axes:
x-axis: Side Length
y-axis: Volume

Key Observations:
The graph indicates a positive correlation between side length and volume.
Specific points include:
At a side length of 4, the volume is 64.
At a side length of 5, the volume is 125.

To identify the pairs of variables that have a linear relationship, we need to analyze each graph based on the provided descriptions and determine if the relationships can be represented by a straight line.

Let's review each pair of variables mentioned:

  1. Side Length and Perimeter of 1 Face

    • As described, when the side length increases, the perimeter increases linearly (e.g., perimeter = 4 * side length). This is a linear relationship.

  2. Perimeter of 1 Face and Area of 1 Face

    • The graph for this relationship suggests a positive correlation, but it may not necessarily represent a linear relationship without more specific data on how perimeter and area change relative to each other. Generally, area increases with an increase in perimeter, but this may not be linear, depending on the shape.

  3. Surface Area and Volume

    • This relationship is generally non-linear for cubes because volume (V) = side length³, and surface area (SA) = 6 * (side length)². Therefore, as surface area increases, volume increases at a different rate (volume scales with the cube of the side length), making it a non-linear relationship.

  4. Area of 1 Face and Surface Area

    • The relationship between the area of one face (A) and surface area (SA) of a cube is linear because surface area = 6 * (side length)², which is directly proportional to the area of one face. When A increases, SA increases proportionally (6 times the area of one face). Thus, this is a linear relationship.

  5. Side Length and Volume

    • This relationship is also non-linear as mentioned previously. The volume scales with the cube of the side length (V = side length³).

Based on the analysis:

Linear Relationships

  1. Side Length and Perimeter of 1 Face
  2. Area of 1 Face and Surface Area

So, the pairs of variables that have a linear relationship are:

  • Side Length and Perimeter of 1 Face
  • Area of 1 Face and Surface Area