Question Sketch the region where $y=2$ .

Studdy Solution

STEP 1

Assumptions
1. We are working in a two-dimensional coordinate system.
2. We are asked to sketch the region defined by the set of points where $y=2$ .

STEP 2

Understand the equation of the set.
The equation $y=2$ defines a set of points in the $xy$ -plane where the $y$ -coordinate is always 2, regardless of the value of the $x$ -coordinate.

STEP 3

Identify the type of graph.
The graph of the equation $y=2$ is a horizontal line because the $y$ -coordinate is constant and the $x$ -coordinate can be any real number.

STEP 4

Sketch the horizontal line.
Draw a straight horizontal line through the point where $y=2$ on the $y$ -axis. This line extends infinitely in both the positive and negative $x$ -directions.

STEP 5

Label the line.
Mark the line with the equation $y=2$ to indicate that every point on this line satisfies the equation.
The region given by the set $\{(x, y) \mid y=2\}$ is a horizontal line at $y=2$ on the coordinate plane.

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Question Sketch the region where $y=2$ .

Studdy Solution

STEP 1

Assumptions
1. We are working in a two-dimensional coordinate system.
2. We are asked to sketch the region defined by the set of points where $y=2$ .

STEP 2

Understand the equation of the set.
The equation $y=2$ defines a set of points in the $xy$ -plane where the $y$ -coordinate is always 2, regardless of the value of the $x$ -coordinate.

STEP 3

Identify the type of graph.
The graph of the equation $y=2$ is a horizontal line because the $y$ -coordinate is constant and the $x$ -coordinate can be any real number.

STEP 4

Sketch the horizontal line.
Draw a straight horizontal line through the point where $y=2$ on the $y$ -axis. This line extends infinitely in both the positive and negative $x$ -directions.

STEP 5

Label the line.
Mark the line with the equation $y=2$ to indicate that every point on this line satisfies the equation.
The region given by the set $\{(x, y) \mid y=2\}$ is a horizontal line at $y=2$ on the coordinate plane.

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Question Sketch the region where y=2y=2y=2.

Studdy Solution

STEP 1

Assumptions1. We are working in a two-dimensional coordinate system.2. We are asked to sketch the region defined by the set of points where y=2y=2y=2.

STEP 2

Understand the equation of the set.The equation y=2y=2y=2 defines a set of points in the xyxyxy-plane where the yyy-coordinate is always 2, regardless of the value of the xxx-coordinate.

STEP 3

Identify the type of graph.The graph of the equation y=2y=2y=2 is a horizontal line because the yyy-coordinate is constant and the xxx-coordinate can be any real number.

STEP 4

Sketch the horizontal line.Draw a straight horizontal line through the point where y=2y=2y=2 on the yyy-axis. This line extends infinitely in both the positive and negative xxx-directions.

STEP 5

Label the line.Mark the line with the equation y=2y=2y=2 to indicate that every point on this line satisfies the equation.The region given by the set {(x,y)∣y=2}\{(x, y) \mid y=2\}{(x,y)∣y=2} is a horizontal line at y=2y=2y=2 on the coordinate plane.

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Question Sketch the region where $y=2$ .

Assumptions
1. We are working in a two-dimensional coordinate system.
2. We are asked to sketch the region defined by the set of points where $y=2$ .

Understand the equation of the set.
The equation $y=2$ defines a set of points in the $xy$ -plane where the $y$ -coordinate is always 2, regardless of the value of the $x$ -coordinate.

Identify the type of graph.
The graph of the equation $y=2$ is a horizontal line because the $y$ -coordinate is constant and the $x$ -coordinate can be any real number.

Sketch the horizontal line.
Draw a straight horizontal line through the point where $y=2$ on the $y$ -axis. This line extends infinitely in both the positive and negative $x$ -directions.

Label the line.
Mark the line with the equation $y=2$ to indicate that every point on this line satisfies the equation.
The region given by the set $\{(x, y) \mid y=2\}$ is a horizontal line at $y=2$ on the coordinate plane.