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Chapter 3: Problem 53

What does it mean if the slope of a line is zero?

Short Answer

Expert verified
A line has a slope of zero when it is a horizontal line. This means there is no vertical change for any horizontal change.

Step by step solution

01

Understanding the concept of slope

The slope of a line, typically represented by the variable \(m\), measures the steepness of the line. It is defined as the ratio of the vertical change to the horizontal change between any two points on the line.
02

Understanding zero slope

A line is said to have a zero slope when it is perfectly horizontal. That is, there is no vertical change for any horizontal change. Therefore, the ratio of 'rise over run' or 'change in y over change in x' is zero (0/any number equals 0). Therefore, a zero slope means a horizontal line.
03

Visual representation

If you plot a horizontal line on a graph, you will notice that it runs parallel to the x-axis, going across without any change in the vertical direction. The horizontal line represents a slope of zero.

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Most popular questions from this chapter

will help you prepare for the material covered in the next section. Remember that a solution of an equation in two variables is an ordered pair. Let \(y=0\) and find a solution of \(3 x-4 y=24\)

Graph equation. \(x+1=0\)

write each sentence as a linear equation in two variables. Then graph the equation. The \(y\) -variable is 3 more than the \(x\) -variable.

Solve for \(h: \quad V=\frac{1}{3} A h .\) (Section 2.4, Example 4)

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=\frac{1}{2} x$$
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