Question

The graph of the equation y = 3 is a

A. Vertical Line
B. Horizontal Line
C. A Point
D. Diagonal Line​

Answer 1

The correct answer to the provided question is B. Horizontal Line. The graph of the equation y = 3 is a horizontal line because it represents all points where y is always 3, regardless of the x-value.

Step-by-step explanation:

The graph of the equation y = 3 is a horizontal line. When a linear equation is in the form y = a, where a is a constant, the graph will be a horizontal line that intersects the y-axis at the value of a. In this case, the line intersects the y-axis at y = 3. It doesn’t matter what value x takes; the value of y will always be 3, creating a line that runs horizontally across the graph.

When discussing the algebra of straight lines, as illustrated in Figure A1, the terms b and m dictate the y-intercept and the slope of the line, respectively. However, because our equation lacks an x term, it has no slope and does not depend on the x value, distinguishing it from cases where a line has a slope, as seen when a line is described by an equation like y = mx + b.

The correct answer to the provided question is B. Horizontal Line.

Answer 2

The graph of the equation y = 3 is a horizontal line. So, the correct option is B. Horizontal Line.

Step-by-step explanation:

The equation y = 3 represents a line where the value of y is constantly 3, regardless of the value of x. This means that for every x-coordinate, the y-coordinate will always be 3. Consequently, the graph will be a straight, horizontal line parallel to the x-axis at y = 3.

This equation, y = 3, doesn't involve any variable depending on x, indicating that the line drawn will be independent of x and remain fixed at y = 3. As a result, it doesn't slope in any direction but remains perfectly horizontal along the y-axis.

In essence, the equation y = 3 represents a constant function where y is always 3. Graphically, this is depicted as a line that doesn't ascend or descend but remains flat at y = 3. Unlike a vertical line (where x is constant), this equation refers to y as constant, resulting in a horizontal line.

Therefore, the graph of the equation y = 3 is a horizontal line that extends infinitely along the y-axis at the value y = 3. This interpretation aligns with the understanding that the equation denotes a fixed value for y, irrespective of any x input, indicating a horizontal orientation in the Cartesian plane.

So, the correct option is B. Horizontal Line.