Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Using the graph, derive the equation of the line in slope-intercept form.

A. y=−3x−4

B. y=3x−4

C. y=3x+4

D. 3x−y=4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope of the line.

The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points provided: (0, -4) and (1, -1)
m = (-1 - (-4)) / (1 - 0)
m = (3) / (1)
m = 3

Now that we have the slope (m = 3), we can use one of the points given to solve for the y-intercept (b). Let's use the point (0, -4).

-4 = 3(0) + b
-4 = 0 + b
b = -4

Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4

The correct answer is option B: y = 3x - 4

Answer 2

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.
Write the equation of the line in slope-intercept form.

A. −5x−y=−1

B. y=−5x+1

C. y=5x+1

D. y=−5x−1

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope of the line.

The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points provided: (0, 1) and (1, -4)
m = (-4 - 1) / (1 - 0)
m = (-5) / (1)
m = -5

Now that we have the slope (m = -5), we can use one of the points given to solve for the y-intercept (b). Let's use the point (0, 1).

1 = -5(0) + b
1 = 0 + b
b = 1

Therefore, the equation of the line in slope-intercept form is:
y = -5x + 1

The correct answer is option B: y = -5x + 1

Answer 4

Graph the linear equation y=−3x+2.

A. 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 2 right parenthesis, and left parenthesis 1 comma negative 1 right parenthesis.

B. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. he line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis. A dotted vertical line labeled 3 from left parenthesis 1 comma negative 5 right parenthesis and a dotted horizontal line labeled 1 from left parenthesis 0 comma negative 2 right parenthesis intersect at left parenthesis 1 comma negative 2 right parenthesis, forming a right triangle with the slope.

C. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.

D. 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 negative 2 comma 2 right parenthesis, and left parenthesis 0 comma 1 right parenthesis.

Answer 5

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

A. 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: (0, 2) and (1, -1).

This matches the given equation y = -3x + 2, where the y-intercept is 2 and the slope is -3. The plotted points align with the equation.

Answer 6

Use the image to answer the question.

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 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4?

A. No, it is not the correct graph because this graph used (0,3) as the y-intercept.

B. No, it is not the correct graph because this graph has a positive slope.

C. Yes, it is the correct graph because this graph has a y-intercept of (0,4).

D. Yes, it is the correct graph because this graph has a y-intercept of (0,3).

Answer 7

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

D. Yes, it is the correct graph because this graph has a y-intercept of (0,3).

The equation given is y = -13x + 4. The y-intercept of the equation is when x = 0, which gives us (0, 4). The graph shown has the correct y-intercept of (0, 3) and based on the slope-intercept form, the slope is indeed -13x, so this is the correct graph for the equation provided.

Answer 8

Graph the linear equation

y=23x−1.

A. 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 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.

B. 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 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.

C. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.

D. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.

Answer 9

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

A. 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: (0, -1), and (3, 1).

This matches the given equation y = 2/3x - 1, where the y-intercept is -1 and the slope is 2/3. The plotted points align with the equation.