Identify the slope and the y -intercept of the equation 4x−3y=12 .(1 point) Responses 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 . The slope is −43, and the y-intercept is (0, 4).

Question

GPT-4o mini · Answer

To find the slope and the y-intercept of the equation \( 4x - 3y = 12 \), we can rearrange the equation into slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the equation:

\[ 4x - 3y = 12 \]

Solve for \( y \):

\[ -3y = -4x + 12 \]

\[ y = \frac{4}{3}x - 4 \]

From this, we can identify:

The slope (\( m \)) is \( \frac{4}{3} \).
The y-intercept (\( b \)) is \( -4 \), which corresponds to the point (0, -4).

Thus, the correct response is:

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

...hi.... · Answer

can you double check your answer??

GPT-4o mini · Answer

Sure! Let's double-check the process for finding the slope and the y-intercept from the equation \( 4x - 3y = 12 \).

Start with the given equation:

\( 4x - 3y = 12 \)
Rearranging it to the slope-intercept form \( y = mx + b \):

First, isolate the term with \( y \):

\[ -3y = -4x + 12 \]

Next, divide every term by -3 to solve for \( y \):

\[ y = \frac{4}{3}x - 4 \]

From this equation:

The slope \( m \) is \( \frac{4}{3} \).
The y-intercept \( b \) is \( -4 \), which corresponds to the point (0, -4).

So, the conclusion remains that:

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

This confirms that the earlier analysis is correct.

...hi.... · Answer

are you still there bot?

GPT-4o mini · Answer

Yes, I'm here! How can I assist you further? If you have more questions or need clarification on something, feel free to ask!

...hi.... · Answer

Which two of the following is an example of a gerund phrase?(1 point) Responses Surprised by the news Surprised by the news The broken vase The broken vase Holding the trophy Holding the trophy Running in the park

GPT-4o mini · Answer

A gerund phrase consists of a gerund (which is a verb ending in -ing that functions as a noun) along with any modifiers or complements. Let's analyze the options:

Surprised by the news - This is not a gerund phrase; it contains a past participle "surprised."
The broken vase - This is a noun phrase describing a vase; it does not contain a gerund.
Holding the trophy - This is a gerund phrase, where "holding" is the gerund and "the trophy" is the object of the gerund.
Running in the park - This is also a gerund phrase, where "running" is the gerund, and "in the park" is a prepositional phrase modifying it.

So, the examples of gerund phrases are:

Holding the trophy
Running in the park

These are the two correct choices.

...hi.... · Answer

Which of the following is an example of a participle phrase?(1 point) Responses His passion for singing His passion for singing Standing by the tree Standing by the tree Reading books Reading books The broken vase

GPT-4o mini · Answer

A participle phrase consists of a participle (a verb form functioning as an adjective) along with any modifiers or complements. Let's analyze the options:

His passion for singing - This is a noun phrase; it does not contain a participle.
Standing by the tree - This is a participle phrase, where "standing" is the present participle and "by the tree" is a prepositional phrase modifying it.
Reading books - This is a gerund phrase, with "reading" functioning as a noun, so it is not a participle phrase.
The broken vase - This is a noun phrase where "broken" is a past participle acting as an adjective describing "vase," but it is not a complete participle phrase.

The correct example of a participle phrase is:

Standing by the tree

This is the only option that fits the definition of a participle phrase.

...hi.... · Answer

Which of the following is an example of a participle used as an adjective?(1 point) Responses They had finished their work before the deadline. They had finished their work before the deadline. The running water soothed her. The running water soothed her. The broken vase lay on the floor. The broken vase lay on the floor. She has already eaten dinner.

GPT-4o mini · Answer

A participle used as an adjective modifies a noun. Let's analyze the options to identify the example of a participle functioning as an adjective:

They had finished their work before the deadline. - "Finished" is a past participle here, but it is part of the verb phrase and does not modify a noun directly in this context.
The running water soothed her. - "Running" is a present participle that modifies the noun "water." This is an example of a participle used as an adjective.
The broken vase lay on the floor. - "Broken" is a past participle that modifies the noun "vase." This is also an example of a participle used as an adjective.
She has already eaten dinner. - "Eaten" is a past participle used as part of the verb phrase and does not modify a noun directly in this context.

Thus, both "The running water soothed her" and "The broken vase lay on the floor" are correct examples of participles used as adjectives. However, since you are looking for a single response:

The best example from the options is: The running water soothed her.

If you need to choose only one, that would be the option to select.