Problem 53 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.