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Chapter 11: Problem 351

Find the slope of the line \(y=2 .\)

Short Answer

Expert verified
The slope of the line \( y = 2 \) is 0.

Step by step solution

01

Identify the given equation

The given equation of the line is in the form of a constant, which is written as: \[ y = 2 \]
02

Understand the form of the line

The equation \( y = 2 \) represents a horizontal line where the value of \( y \) is always 2, regardless of the value of \( x \).
03

Identify the slope of a horizontal line

The slope of a horizontal line is always 0. This is because there is no change in the \( y \) value as \( x \) changes.
04

Conclusion

Therefore, the slope of the line given by the equation \( y = 2 \) is 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

horizontal line
When we talk about a horizontal line, we are referring to a line that runs left to right and is parallel to the x-axis. The most crucial characteristic of a horizontal line is that no matter the value of x, the value of y remains constant.

For example, in the equation \( y = 2 \), y is always 2 no matter what x is.
  • Horizontal lines have a steady y-value
  • They show no vertical change
  • The equation often looks like \( y = c \), where c is a constant
Understanding this will help when identifying the form of a line in linear equations.
constant equation
A constant equation typically means its value does not change. For linear equations, if we see something like \[ y = 2 \], it indicates that for every point on this line, y will always be 2.
By identifying this, it becomes clear that we are dealing with a special kind of line:
  • It's constant in its value
  • It results in a horizontal line
  • The term 'constant' signifies that one of the variables (in this case y) does not change
So, whenever you see an equation in the format \( y = \text{constant} \), you can think of a straight, unchanging line.
zero slope
Slope measures how steep a line is. Specifically, it shows how much y changes as x changes.
For horizontal lines, like \( y = 2 \), there's no vertical change, meaning the line doesn't rise or fall; it stays completely level. Hence, the 'slope' of such a line is zero.

The mathematical representation of slope (\textbackslash frac{\text{rise}}{\text{run}}) hence gives: \[ \text{Slope} = \frac{0}{\text{run}} = 0 \]
  • Zero slope indicates a level line
  • No change in y with changes in x
  • Graphically, means the line stays the same horizontally
Understanding zero slope is essential for distinguishing between different kinds of lines in coordinate geometry.

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Most popular questions from this chapter

Road grade A local road has a grade of 6\(\% .\) The grade of a road is its slope expressed as a percent. (a) Find the slope of the road as a fraction and then simplify the fraction. (b) What rise and run would reflect this slope or grade?

In the following exercises, graph the line given a point and the slope. $$ (-1,0) ; m=\frac{1}{5} $$

In the following exercises, graph each equation. $$ y=-x $$

In the following exercises, graph each equation. $$ x-y=3 $$

In the following exercises, graph each equation. $$ y=5 $$
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