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

Answer 1

[AI-generated answer — Bot GPT 3.5]

The illustration on the coordinate plane would look like this:

-------------------------------------
| |
| |
| |
| |
| |
| |
| ↑ |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|--------------------------------------|

Here, the x-axis ranges from -9 to 9 and the y-axis ranges from -11 to 11. The coordinates (0, -4) and (1, -1) are plotted as points on the solid upward line that passes through them. The line extends infinitely in both directions with arrows at both ends to indicate that.

Answer 2

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.

(1 point)
Responses

y=−3x−4
y equals negative 3 x minus 4

y=3x+4
y equals 3 x plus 4

3x−y=4
3 x minus y equals 4

y=3x−4
y equals 3 x minus 4

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we need to determine the slope of the line and the y-intercept.

The slope of a line passing through two points, (x1, y1) and (x2, y2), is given by the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Using the given points (0, -4) and (1, -1), we can calculate the slope:

m = (-1 - (-4)) / (1 - 0) = 3/1 = 3

Next, we need to find the y-intercept (b), which is the value of y when x = 0.

From the given point (0, -4), we can see that -4 is the y-intercept.

Therefore, the equation of the line in slope-intercept form is:

y = 3x - 4

Answer 4

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.

Answer 5

[AI-generated answer — Bot GPT 3.5]

The illustration on the coordinate plane would look like this:

-------------------------------------
| |
| |
| |
| |
| |
| |
| ↓ |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|--------------------------------------|

Here, the x-axis ranges from -9 to 9 and the y-axis ranges from -11 to 11. The coordinates (0, 1) and (1, -4) are plotted as points on the solid downward line that passes through them. The line extends infinitely in both directions with arrows at both ends to indicate that.

To find the equation of the line in slope-intercept form, we need to determine the slope of the line and the y-intercept.

The slope of a line passing through two points, (x1, y1) and (x2, y2), is given by the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Using the given points (0, 1) and (1, -4), we can calculate the slope:

m = (-4 - 1) / (1 - 0) = -5/1 = -5

Next, we need to find the y-intercept (b), which is the value of y when x = 0.

From the given point (0, 1), we can see that 1 is the y-intercept.

Therefore, the equation of the line in slope-intercept form is:

y = -5x + 1

Answer 6

Graph the linear equation y=−3x+2.(1 point)

Responses
A) 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.

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

C) 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.

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 0 comma 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.

Answer 7

[AI-generated answer — Bot GPT 3.5]

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

Answer 8

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=−1/3x+4?(1 point)
Responses

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

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

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

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

Answer 9

[AI-generated answer — Bot GPT 3.5]

No, it is not the correct graph because this graph has a positive slope and the equation y = -1/3x + 4 has a negative slope.

Answer 10

Graph the linear equation

y=2/3x−1.

(1 point)
Responses
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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 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 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis. "/>

Answer 11

[AI-generated answer — Bot GPT 3.5]

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