Questions: QUESTION 23 What does the graph of the equation (y=2) look like? What is its slope? - Horizontal line; slope is undefined - Horizontal line; slope (=0) - Vertical line; slope is undefined - Vertical line; slope (=0)

QUESTION 23

What does the graph of the equation (y=2) look like? What is its slope?
- Horizontal line; slope is undefined
- Horizontal line; slope (=0)
- Vertical line; slope is undefined
- Vertical line; slope (=0)

Transcript text: QUESTION 23 What does the graph of the equation $y=2$ look like? What is its slope? Horizontal line; slope is undefined Horizontal line; slope $=0$ Vertical line; slope is undefined Vertical line; slope $=0$

Solution

Solution Steps

To determine the graph of the equation $ y = 2 $ and its slope, we need to understand the nature of the equation. The equation $ y = 2 $ represents a horizontal line where the y-coordinate is always 2, regardless of the x-coordinate. The slope of a horizontal line is 0 because there is no vertical change as the x-coordinate changes.

Solution Approach

Recognize that $ y = 2 $ is a horizontal line.
The slope of a horizontal line is 0.

Step 1: Identify the Equation

The equation given is $ y = 2 $. This represents a line where the y-coordinate is constant at 2 for all values of $ x $.

Step 2: Describe the Graph

The graph of the equation $ y = 2 $ is a horizontal line that intersects the y-axis at the point $ (0, 2) $. This means that for any value of $ x $, the value of $ y $ will always be 2.

Step 3: Determine the Slope

The slope of a line is defined as the change in $ y $ divided by the change in $ x $. For a horizontal line, there is no change in $ y $ as $ x $ changes, which results in a slope of $ 0 $. Therefore, the slope of the line represented by the equation $ y = 2 $ is $ 0 $.