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Chapter 1: Problem 137

Determine whether the statement is true or false. Justify your answer. A line with a slope of \(-\frac{5}{7}\) is steeper than a line with a slope of \(-\frac{6}{7}\).

Short Answer

Expert verified
The statement is false. The line with a slope of \(-\frac{6}{7}\) is steeper than the line with a slope of \(-\frac{5}{7}\).

Step by step solution

01

Understanding Slope

The slope of a line is a measure of its steepness. It is represented by the letter \(m\) and can be positive, negative, or zero. The greater the absolute value of the slope, the steeper the line. Also, a positive slope results in a line that ascends from left to right, while a negative slope results in a line that descends from left to right.
02

Comparing Slopes

We have two slopes to compare: \(-\frac{5}{7}\) and \(-\frac{6}{7}\). The negative sign indicates that both lines descend from left to right. When comparing these slopes, we look at their absolute values, since we're interested in their steepness, not their direction. The absolute value of \(-\frac{5}{7}\) is \(\frac{5}{7}\) and the absolute value of \(-\frac{6}{7}\) is \(\frac{6}{7}\). Since \(\frac{5}{7} < \frac{6}{7}\), the line with slope \(-\frac{5}{7}\) is less steep than the line with slope \(-\frac{6}{7}\).
03

Statement Evaluation

Therefore, the statement 'A line with a slope of \(-\frac{5}{7}\) is steeper than a line with a slope of \(-\frac{6}{7}\)' is false, because the absolute value of \(-\frac{5}{7}\) is less than the absolute value of \(-\frac{6}{7}\), indicating that the line with slope \(-\frac{5}{7}\) is less steep.

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Most popular questions from this chapter

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