Chapter 8.6, Problem 24HP

To determine

To explain:Whether a horizontal line is always, sometimes, or never has 0slope.

Answer to Problem 24HP

When the line is horizontal then slope of the line is always zero.

Explanation of Solution

Given:

  $y=1$

Calculation:

Consider the graph that is parallel to x - axis means that line is horizontal and y=1

Slope is the ratio of the rise or the vertical change, to the run, or the horizontal change.

Since, the value of y-axis is constant. It means the value of y does not changes.

And, we know that:

  $\text{slope=}\frac{\text{change in y}}{\text{change in x}}$

And, change in y is 0.

So,

  $\begin{array}{l}\text{slope=}\frac{\text{0}}{\text{change in x}}\\ =0\end{array}$

Therefore, when the line is horizontal then slope of the line is always zero.

Conclusion:

Therefore, when the line is horizontal then slope of the line is always zero.