Interpret the equation y=−4x+10 . What type of function does this equation define? Describe its graph.(1 point) Responses This is a nonlinear function. Its graph has a maximum at (0,10) . This is a nonlinear function. Its graph has a maximum at left parenthesis 0 comma 10 right parenthesis . This is a linear function. Its graph is a straight line with a y -intercept of −4 and a slope of 10. This is a linear function. Its graph is a straight line with a y -intercept of negative 4 and a slope of 10. This is a linear function. Its graph is a straight line with a slope of −4 and a y -intercept of 10. This is a linear function. Its graph is a straight line with a slope of negative 4 and a y -intercept of 10. This is a nonlinear function. Its graph is a curve.

Question

GPT-4o mini · Answer

The equation $ y = -4x + 10 $ defines a linear function. - **Type of Function**: It is a linear function because it can be written in the form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. In this case, the slope $ m $ is $-4$ and the y-intercept $ b $ is $10$. - **Description of the Graph**: The graph of this linear function is a straight line. The slope of $-4$ indicates that for every unit increase in $ x $, the value of $ y $ decreases by $4$. The line crosses the y-axis at the point $(0, 10)$. Therefore, the correct response would be: "This is a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10."

...hi.... · Answer

The equation of a function is y=2x−6 . If this function were graphed, what would its y -intercept be?(1 point) Responses −3 negative 3 −6 negative 6 6 6 2

GPT-4o mini · Answer

To find the y-intercept of the function given by the equation $ y = 2x - 6 $, we can determine the value of $ y $ when $ x = 0 $.

Substituting $ x = 0 $ into the equation:

\[ y = 2(0) - 6 = -6 \]

Thus, the y-intercept of the function is $-6$.

Therefore, the correct response is: −6.

...hi.... · Answer

Use the table to answer the question. x y 4 38 6 58 Write the equation of the linear function that models the relationship shown in the table. (1 point) Responses y=x+34 y equals x plus 34 y=10x+2 y equals 10 x plus 2 y=−10x+78 y equals negative 10 x plus 78 y=10x−2

GPT-4o mini · Answer

To find the equation of the linear function that models the relationship given in the table, we can use the two points provided: (4, 38) and (6, 58).

Calculate the slope (m): The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (4, 38) and (6, 58):

\[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]

Use the point-slope form to find the equation: We can use one of the points, let’s use (4, 38), and the slope we just calculated. The point-slope form of the equation is:

\[ y - y_1 = m(x - x_1) \]

Substituting in the values:

\[ y - 38 = 10(x - 4) \]

Simplify the equation:

First, distribute the slope:

\[ y - 38 = 10x - 40 \]

Now, add 38 to both sides:

\[ y = 10x - 40 + 38 \]

\[ y = 10x - 2 \]

Therefore, the equation of the linear function that models the relationship shown in the table is:

y = 10x − 2.

...hi.... · Answer

Oliwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.(1 point) Responses y=1,000x+3 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y equals 1,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y=3x+3,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y equals 3 x plus 3,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y=3x+1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y equals 3 x plus 1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y=3,000x+3 , where x is the number of months and y is the total amount of money Oliwia will have in her account. y equals 3,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

GPT-4o mini · Answer

To model the relationship between the number of months and the total amount of money in Oliwia's bank account, we start with her initial deposit and the interest she earns each month.

Initial Deposit: Oliwia deposits $3,000.
Monthly Interest: She earns $3 in interest per month.

Let $ x $ represent the number of months, and $ y $ represent the total amount of money in her account after $ x $ months.

The total amount of money $ y $ can be expressed as:

\[ y = \text{initial deposit} + \text{(monthly interest)} \times x \]

Substituting the initial deposit and the interest:

\[ y = 3000 + 3x \]

Thus, the equation that models the relationship is:

\[ y = 3x + 3000 \]

So, the correct response is:

y = 3x + 3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.

...hi.... · Answer

still there bot?

GPT-4o mini · Answer

Yes, I'm here! How can I assist you further?

...hi.... · Answer

Which phrase describes a context clue?(1 point) Responses resources that help the reader determine the origin of a word resources that help the reader determine the origin of a word words or phrases in a text that help the reader determine the meaning of a word words or phrases in a text that help the reader determine the meaning of a word words or phrases in a text that help the reader determine where to find the definition of a word words or phrases in a text that help the reader determine where to find the definition of a word resources that help the reader determine the pronunciation of a word resources that help the reader determine the pronunciation of a word

GPT-4o mini · Answer

The phrase that best describes a context clue is:

"words or phrases in a text that help the reader determine the meaning of a word."

Context clues are hints found within a sentence or paragraph that can help readers understand the meaning of unfamiliar words.