Transform the linear equation −2y=14−6x

Question

to slope-intercept form.(1 point)
y=

Write 0.4x+0.2y=0.6
in slope-intercept form.(1 point)
y=

Write the linear equation 3y=6x−18
in slope-intercept form.(1 point)

What is the slope and the y
-intercept of the equation 9+272x=−32y
. Write the y
-intercept as an ordered pair.(1 point)
The slope is
. The y
-intercept is (

Answer 1

Let's transform each of the given equations to slope-intercept form (which has the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept).

1. Transforming \(-2y = 14 - 6x\): \[ -2y = -6x + 14 \] Now, divide by -2: \[ y = 3x - 7 \] So in slope-intercept form: \[ y = 3x - 7 \]

2. Transforming \(0.4x + 0.2y = 0.6\): \[ 0.2y = -0.4x + 0.6 \] Now, divide by 0.2: \[ y = -2x + 3 \] So in slope-intercept form: \[ y = -2x + 3 \]

3. Transforming \(3y = 6x - 18\): \[ y = 2x - 6 \] So in slope-intercept form: \[ y = 2x - 6 \]

4. For the equation \(9 + 272x = -32y\): First, rearrange it: \[ -32y = -272x - 9 \] Now, divide by -32: \[ y = \frac{272}{32}x + \frac{9}{32} \] Simplifying \(\frac{272}{32} = 8.5\), we have: \[ y = 8.5x + \frac{9}{32} \] Therefore, the slope is \(8.5\) and the y-intercept is \(\left(0, \frac{9}{32}\right)\).

In summary:

• The slope is 8.5.
• The y-intercept as an ordered pair is \(\left(0, \frac{9}{32}\right)\).

Answer 2

Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)
Responses

−8y=−4x+24
negative 8 y equals negative 4 x plus 24

y=12x−3
y equals Start Fraction 1 over 2 End Fraction x minus 3

4x−8y−24=0
4 x minus 8 y minus 24 equals 0

4x−8y=24

Write y−2=32(x+2) in slope-intercept form.(1 point)
Responses

y=32x+32
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=32+5x
y equals Start Fraction 3 over 2 End Fraction plus 5 x

y=32x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=32x+6
y equals Start Fraction 3 over 2 End Fraction x plus 6

Graph the equation 9−x=32y using slope-intercept form.(1 point)
Responses

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 7 comma negative 1 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 7 comma negative 1 right parenthesis.

A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.
Image with alt text: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.

An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 6 right parenthesis and left parenthesis 3 comma 4 right parenthesis.
Image with alt text: An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 6 right parenthesis and left parenthesis 3 comma 4 right parenthesis.

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 4 comma 2 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 4 comma 2 right parenthesis.
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Question
Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 10 right parenthesis and left parenthesis 1 comma negative 7 right parenthesis.

Is this the correct graph of 3x−y=10 ?

(1 point)
Responses

Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10).
Yes, it is the correct graph because the slope is negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .

No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10).
No, it is not the correct graph because the slope is 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .

Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).
Yes, it is the correct graph because the slope is 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .

No, it is not the correct graph because the slope is −3 and the y-intercept is (0, −10).
No, it is not the correct graph because the slope is negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .
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Question
Identify the slope and the y-intercept of the equation 4x−3y=12.(1 point)
Responses

The slope is −43, and the y-intercept is (0, 4).
The slope is negative Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma 4 right parenthesis .

The slope is 4, and the y-intercept is (0, 12).
The slope is 4, and the y-intercept is left parenthesis 0 comma 12 right parenthesis .

The slope is 43, and the y-intercept is (0, 4).
The slope is Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma 4 right parenthesis .

The slope is 43, and the y-intercept is (0, −4).
The slope is Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma negative 4 right parenthesis .
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Answer 3

Let’s solve each of these problems step by step.

1. Transform the linear equation \(4x - 8y = 24\) to slope-intercept form.

Starting with: \[ 4x - 8y = 24 \]

Rearranging gives us: \[ -8y = -4x + 24 \]

Now divide every term by \(-8\): \[ y = \frac{1}{2}x - 3 \]

The final slope-intercept form is:

\[ y = \frac{1}{2}x - 3 \]

2. Write \(y - 2 = 32(x + 2)\) in slope-intercept form.

Distributing \(32\): \[ y - 2 = 32x + 64 \]

Now add \(2\) to both sides: \[ y = 32x + 66 \]

The final slope-intercept form is:

\[ y = 32x + 66 \]

3. Graph the equation \(9 - x = 32y\) using slope-intercept form.

Start by rearranging the equation: \[ 32y = -x + 9 \]

Dividing by \(32\): \[ y = -\frac{1}{32}x + \frac{9}{32} \]

The slope is:

\(-\frac{1}{32}\)

And the y-intercept is:

\(\left(0, \frac{9}{32}\right)\)

4. Is the graph correct for \(3x - y = 10\)?

To put \(3x - y = 10\) in slope-intercept form: \[ y = 3x - 10 \]

This means:

• Slope = 3
• y-intercept = (0, -10)

The line described in the illustration passes through the points \((0, -10)\) and \((1, -7)\), which has a slope of 3.

The correct answer is:

Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).

5. Identify the slope and y-intercept of the equation \(4x - 3y = 12\).

Rearranging: \[ -3y = -4x + 12 \] Dividing by \(-3\): \[ y = \frac{4}{3}x - 4 \]

The slope is:

\(\frac{4}{3}\)

The y-intercept is:

\((0, -4)\)

Therefore, the correct response is:

The slope is \(\frac{4}{3}\), and the y-intercept is \((0, -4)\).

Answer 4

Write y−2=3/2(x+2) in slope-intercept form.(1 point)
Responses

y=3/2x+3/2
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=3/2+5x
y equals Start Fraction 3 over 2 End Fraction plus 5 x

y=3/2x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=3/2x+6

Answer 5

To rewrite the equation \(y - 2 = \frac{3}{2}(x + 2)\) in slope-intercept form (which is \(y = mx + b\)), follow these steps:

1. Distribute \(\frac{3}{2}\): \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] \[ y - 2 = \frac{3}{2}x + 3 \]

2. Add \(2\) to both sides: \[ y = \frac{3}{2}x + 3 + 2 \] \[ y = \frac{3}{2}x + 5 \]

The final slope-intercept form is:

\[ y = \frac{3}{2}x + 5 \]

Therefore, the correct response is:

y = \frac{3}{2}x + 5.

Answer 6

Use the table to answer the question.

Day Observations
1 sunny and warm
2 cloudy and rainy
3 drop in temperature
4 clear skies and cold temperatures
A student tracks the daily weather. The student’s observations are logged in the table. Which factor in the atmosphere best explains the student’s observations?

(1 point)
Responses

High levels of moisture are contained within an air mass.
High levels of moisture are contained within an air mass.

A warm air mass replaced a cold air mass.
A warm air mass replaced a cold air mass.

A cold front moved into the area.
A cold front moved into the area.

A warm front moved into the area.
A warm front moved into the area.
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A meteorologist uses a weather map to explain an upcoming change in weather. The map shows a blue line with triangles approaching a red line with semicircles. Based on the map, which weather prediction is most valid? (1 point)
Responses

A significant drop in temperature will occur across the area.
A significant drop in temperature will occur across the area.

There is no chance of precipitation in the forecast.
There is no chance of precipitation in the forecast.

Warm temperatures will replace cold temperatures.
Warm temperatures will replace cold temperatures.

Humidity levels will rise.

Which factor in the atmosphere is most responsible for changes in an area’s temperatures and humidity levels?(1 point)
Responses

different types of cloud formations
different types of cloud formations

density of air
density of air

movement of large air masses
movement of large air masses

amount of precipitation

Use the weather forecast from a meteorologist to answer the question.

“Temperatures will plummet late Thursday night through Saturday. All areas across the eastern region of the state are anticipated to be below freezing by Friday morning and again on Saturday morning. Heavy amounts of snow are possible late Thursday into Friday. High winds can also be expected across the area.”

Which news headline best accounts for this change in weather?

(1 point)
Responses

“A Strong Cold Front Threatens the Region”
“A Strong Cold Front Threatens the Region”

“A Warm Front Blankets the Region”
“A Warm Front Blankets the Region”

“A Warm Air Mass Forms over the Region”
“A Warm Air Mass Forms over the Region”

“A Cold Air Mass Exits the Region”

Which condition would most likely require the National Weather Service to issue a severe thunderstorm warning?(1 point)
Responses

a front moving out of an area
a front moving out of an area

an air mass developing over a large body of water
an air mass developing over a large body of water

a large amount of moisture in the air condensing to form clouds
a large amount of moisture in the air condensing to form clouds

a meeting of two air masses with major differences in temperature and moisture

Answer 7

Here are the answers to your questions based on the provided information:

1. Which factor in the atmosphere best explains the student’s observations?

   • A cold front moved into the area.
     • This is suggested by the observations indicating a drop in temperature and a transition from warm, sunny conditions to cold conditions, which is typically associated with the passage of a cold front.

2. Based on the weather map with a blue line with triangles approaching a red line with semicircles, which weather prediction is most valid?

   • A significant drop in temperature will occur across the area.
     • A blue line with triangles indicates a cold front, which typically brings a decrease in temperatures as it moves through an area.

3. Which factor in the atmosphere is most responsible for changes in an area’s temperatures and humidity levels?

   • Movement of large air masses.
     • The movement of air masses is a primary driver of changes in temperature and humidity.

4. Which news headline best accounts for the change in weather?

   • “A Strong Cold Front Threatens the Region.”
     • The forecast describes dropping temperatures and the possibility of heavy snow, which are typically associated with a strong cold front.

5. Which condition would most likely require the National Weather Service to issue a severe thunderstorm warning?

   • A meeting of two air masses with major differences in temperature and moisture.
     • This scenario often leads to the development of severe thunderstorms as the contrasting air masses interact.

These responses should accurately reflect the atmospheric conditions described in your questions!

Answer 8

Which statement is an example of a good piece of evidence?(1 point)
Responses

My family owns a dog.
My family owns a dog.

In a recent study, only 12% of students enjoy volunteering.
In a recent study, only 12% of students enjoy volunteering.

Yellow is a calming color.
Yellow is a calming color.

I believe our local football team is the best.

How can text features help the reader delineate an author's argument?(1 point)
Responses

Text features interest the reader.
Text features interest the reader.

Text features reveal the main points to the reader.
Text features reveal the main points to the reader.

Text features prove the author is lying to the reader.
Text features prove the author is lying to the reader.

Text features persuade the reader.

Read the excerpt from Patrick Henry’s speech “Give Me Liberty or Give Me Death.” What is the main rhetorical device used in the excerpt?

I know of no way of judging of the future but by the past. And judging by the past, I wish to know what there has been in the conduct of the British ministry for the last ten years to justify those hopes with which gentlemen have been pleased to solace themselves and the House.

(1 point)
Responses

hyperbole
hyperbole

rhetorical question
rhetorical question

juxtaposition
juxtaposition

analogy

Read the excerpt from Patrick Henry’s speech “Give Me Liberty or Give Me Death.” What is the author’s purpose for using the rhetorical device you identified in the excerpt?

I know of no way of judging of the future but by the past. And judging by the past, I wish to know what there has been in the conduct of the British ministry for the last ten years to justify those hopes with which gentlemen have been pleased to solace themselves and the House.

(1 point)
Responses

To ask a question for dramatic effect
To ask a question for dramatic effect

To explain a new idea using familiar terms
To explain a new idea using familiar terms

To help readers understand the difference between judgment and justification
To help readers understand the difference between judgment and justification

To make a clear connection between the past and the future

Answer 9

Here are the answers to your questions:

1. Which statement is an example of a good piece of evidence?

   • In a recent study, only 12% of students enjoy volunteering.
     • This statement presents a specific statistic that can be verified and used to support an argument, making it a strong piece of evidence.

2. How can text features help the reader delineate an author's argument?

   • Text features reveal the main points to the reader.
     • Text features like headings, bullet points, and charts help highlight the key arguments and ideas in a text.

3. What is the main rhetorical device used in the excerpt from Patrick Henry’s speech?

   • Rhetorical question.
     • The phrase "I wish to know what there has been in the conduct of the British ministry for the last ten years to justify those hopes..." implies a question, prompting critical thought about the situation without actually posing a direct question.

4. What is the author’s purpose for using the rhetorical device you identified in the excerpt?

   • To make a clear connection between the past and the future.
     • By referencing the past, Henry emphasizes the lack of justification for any hopeful feelings toward the British ministry, suggesting a continuation of negative trends into the future.

These responses should accurately reflect the concepts being asked in your questions!