Question
page 10 of 10
Question 1
A)Please match the following :(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Slope Formula
Which letter represents slope?
Which letter represents the y-intercept?
Slope-intercept Form
y=mx+b
y
=
m
x
+
b
m
m
m=y2−y1x2−x1
m
=
y
2
−
y
1
x
2
−
x
1
b
b
Question 2
A)
Complete the table for the function y=12x+4
y
=
1
2
x
+
4
(1 point)
$$$$$$$$
Question 3
A)
The table represents some points on the graph of a linear function. Write a function that represents this relationship.
(1 point)
y=
y
=
$$
Question 4
A)
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
Based on the table, which function models this situation?
(1 point)
Responses
f(n)=−3n+24
f
(
n
)
=
−
3
n
+
24
f of n is equal to negative 3 n plus 24
f(n)=−13n+16
f
(
n
)
=
−
1
3
n
+
16
f of n is equal to negative 1 third n plus 16
f(n)=−3n+64
f
(
n
)
=
−
3
n
+
64
f of n is equal to negative 3 n plus 64
f(n)=−13n+8
f
(
n
)
=
−
1
3
n
+
8
f of n is equal to negative 1 third n plus 8
Question 5
A)
The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.
Based on the table, which function represents this situation?
(1 point)
Responses
f(x)=3x+7
f
(
x
)
=
3
x
+
7
f of x is equal to 3 x plus 7
f(x)=−7x−3
f
(
x
)
=
−
7
x
−
3
f of x is equal to negative 7 x minus 3
f(x)=−3x
f
(
x
)
=
−
3
x
f of x is equal to negative 3 x
f(x)=7x+3
f
(
x
)
=
7
x
+
3
f of x is equal to 7 x plus 3
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
Question 1
A)Please match the following :(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Slope Formula
Which letter represents slope?
Which letter represents the y-intercept?
Slope-intercept Form
y=mx+b
y
=
m
x
+
b
m
m
m=y2−y1x2−x1
m
=
y
2
−
y
1
x
2
−
x
1
b
b
Question 2
A)
Complete the table for the function y=12x+4
y
=
1
2
x
+
4
(1 point)
$$$$$$$$
Question 3
A)
The table represents some points on the graph of a linear function. Write a function that represents this relationship.
(1 point)
y=
y
=
$$
Question 4
A)
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
Based on the table, which function models this situation?
(1 point)
Responses
f(n)=−3n+24
f
(
n
)
=
−
3
n
+
24
f of n is equal to negative 3 n plus 24
f(n)=−13n+16
f
(
n
)
=
−
1
3
n
+
16
f of n is equal to negative 1 third n plus 16
f(n)=−3n+64
f
(
n
)
=
−
3
n
+
64
f of n is equal to negative 3 n plus 64
f(n)=−13n+8
f
(
n
)
=
−
1
3
n
+
8
f of n is equal to negative 1 third n plus 8
Question 5
A)
The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.
Based on the table, which function represents this situation?
(1 point)
Responses
f(x)=3x+7
f
(
x
)
=
3
x
+
7
f of x is equal to 3 x plus 7
f(x)=−7x−3
f
(
x
)
=
−
7
x
−
3
f of x is equal to negative 7 x minus 3
f(x)=−3x
f
(
x
)
=
−
3
x
f of x is equal to negative 3 x
f(x)=7x+3
f
(
x
)
=
7
x
+
3
f of x is equal to 7 x plus 3
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
Answers
Answered by
GPT-4o mini
Certainly! Let's go through the questions one by one.
### Question 1
**Match the following:**
- **Slope Formula:** \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
- Which letter represents slope? **m**
- Which letter represents the y-intercept? **b** (in the context of the slope-intercept form)
- **Slope-intercept Form:** \( y = mx + b \)
- **m:** represents slope
- **b:** represents y-intercept
### Question 2
**Complete the table for the function \( y = \frac{1}{2}x + 4 \):**
You will need to plug in different values of \( x \) into the equation to find corresponding \( y \) values. For example:
- If \( x = 0 \), then \( y = \frac{1}{2}(0) + 4 = 4 \)
- If \( x = 2 \), then \( y = \frac{1}{2}(2) + 4 = 5 \)
- If \( x = 4 \), then \( y = \frac{1}{2}(4) + 4 = 6 \)
You can create a table with \( x \) values like 0, 2, 4, etc., and calculate the corresponding \( y \).
### Question 3
**Write a function that represents the relationships shown in the table for a linear function.** You will need to identify two points from the table (say (x1, y1) and (x2, y2)) and use the slope formula to find the function:
1. Calculate slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Use the equation of line \( y = mx + b \) to find the intercept \( b \).
**Example**:
Assuming from the table you derived \( m = 2 \) and \( b = 3 \), the function would be:
- \( y = 2x + 3 \).
### Question 4
**Based on the table, which function models this situation?**
If the table shows that the amount of pet food decreases by a certain rate for each meal dispensed (let's say 3 cups per meal), you would choose:
- **f(n) = -3n + 24**
Adjust based on values you find.
### Question 5
**Based on the table, which function represents this situation?**
Similar to Question 4, if the average height of trees increases by a certain rate per year of growth, you would identify the function that correctly matches that linear growth. If from the table you find it increases by 3 feet every year, then:
- **f(x) = 3x + 7** could be the correct model.
Choose based on calculated values.
If you need more specific tables or need to analyze data from the tables, please provide additional details!
### Question 1
**Match the following:**
- **Slope Formula:** \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
- Which letter represents slope? **m**
- Which letter represents the y-intercept? **b** (in the context of the slope-intercept form)
- **Slope-intercept Form:** \( y = mx + b \)
- **m:** represents slope
- **b:** represents y-intercept
### Question 2
**Complete the table for the function \( y = \frac{1}{2}x + 4 \):**
You will need to plug in different values of \( x \) into the equation to find corresponding \( y \) values. For example:
- If \( x = 0 \), then \( y = \frac{1}{2}(0) + 4 = 4 \)
- If \( x = 2 \), then \( y = \frac{1}{2}(2) + 4 = 5 \)
- If \( x = 4 \), then \( y = \frac{1}{2}(4) + 4 = 6 \)
You can create a table with \( x \) values like 0, 2, 4, etc., and calculate the corresponding \( y \).
### Question 3
**Write a function that represents the relationships shown in the table for a linear function.** You will need to identify two points from the table (say (x1, y1) and (x2, y2)) and use the slope formula to find the function:
1. Calculate slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Use the equation of line \( y = mx + b \) to find the intercept \( b \).
**Example**:
Assuming from the table you derived \( m = 2 \) and \( b = 3 \), the function would be:
- \( y = 2x + 3 \).
### Question 4
**Based on the table, which function models this situation?**
If the table shows that the amount of pet food decreases by a certain rate for each meal dispensed (let's say 3 cups per meal), you would choose:
- **f(n) = -3n + 24**
Adjust based on values you find.
### Question 5
**Based on the table, which function represents this situation?**
Similar to Question 4, if the average height of trees increases by a certain rate per year of growth, you would identify the function that correctly matches that linear growth. If from the table you find it increases by 3 feet every year, then:
- **f(x) = 3x + 7** could be the correct model.
Choose based on calculated values.
If you need more specific tables or need to analyze data from the tables, please provide additional details!