Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

This is a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10.

Answer 2

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

Responses

6
6

2
2

−6
negative 6

−3

Answer 3

[AI-generated answer — Bot GPT 3.5]

-6

Answer 4

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=10x+2
y equals 10 x plus 2

y=10x−2
y equals 10 x minus 2

y=x+34
y equals x plus 34

y=−10x+78

Answer 5

[AI-generated answer — Bot GPT 3.5]

Using the values from the table, we see that the slope is (58-38)/(6-4) = 20/2 = 10. We can choose the point (4, 38) to calculate the y-intercept: 38=10(4)+b, b = -2. Therefore, the equation of the linear function is y = 10x - 2.

The correct response is:
y = 10x - 2

Answer 6

Question

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=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=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=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.

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.

Answer 7

[AI-generated answer — Bot GPT 3.5]

The initial deposit Oliwia makes is $3,000, and she earns $3 in interest per month. Since she makes no additional deposits or withdrawals, the total amount of money, y, she will have in her account after x months can be represented by the equation: y = 3x + 3,000.

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.

Answer 8

Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 3 to 3 in one unit increments. The y-axis ranges from negative 3 to 6 in one unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 1 comma 4 right parenthesis and left parenthesis 1 comma 0 right parenthesis.

Write the equation of the linear function shown on the graph.

(1 point)
Responses

y=−2x−2
y equals negative 2 x minus 2

y=2x+2
y equals 2 x plus 2

y=−2x+2
y equals negative 2 x plus 2

y=2x−2

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the equation of the linear function, we can calculate the slope using the two points provided (–1, 4) and (1, 0):

Slope (m) = (y_2 - y_1) / (x_2 - x_1)
Slope (m) = (0 - 4) / (1 - (-1)) = -4 / 2 = -2

Using the point-slope form of the equation of a line, y - y_1 = m(x - x_1), plugging in one of the points, say (1, 0):
y - 0 = -2(x - 1)
y = -2x + 2

Therefore, the correct response is:
y = -2x + 2