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Chapter 6: Problem 91

Determine whether the statement is true or false. Justify your answer. The inclination of a line is the angle between the line and the \(x\) -axis.

Short Answer

Expert verified
The statement is true.

Step by step solution

01

Understand key terms

To find the solution, we need to know the definition of two key terms: inclination of a line and the x-axis. The inclination of a line is the angle which the line makes with the positive direction of the x-axis, often measured counter-clockwise from the positive x-axis. The x-axis is the horizontal axis of a two-dimensional Cartesian coordinate system.
02

Determine the relationship

With the definitions clarified, we can analyze the relationship between the two. If a line is horizontal, it coincides with the x-axis and the inclination is 0. For other cases, the inclination is the angle between the line and the x-axis, measured counter-clockwise from the positive x-axis.
03

Formulate your conclusion

Given the definitions and relationship described, we can now see that the statement: 'The inclination of a line is the angle between the line and the x-axis' is true.

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