Question

Find the angle of inclination of a line with the given slope. You may use a calculator. $$ -1 $$

Short answer

The angle of inclination for a line with the slope of -1 is either -45° or 135°.

Step-by-step solution

Write down the given slope

We are given the slope of the line as \(m = -1\).

Calculate the angle of inclination using the arctangent function

We will use the formula: Angle of inclination (θ) = \(tan^{-1}(m)\) Plug in the given slope, \(m = -1\): θ = \(tan^{-1}(-1)\)

Calculate θ using a calculator

Now, use the calculator to find the arctangent of -1: θ = \(tan^{-1}(-1)\) ≈ -45°

Convert the negative angle to the equivalent positive angle, if necessary

If you prefer to express the angle of inclination as a positive angle, you can add 180° to the negative angle obtained earlier: θ = -45° + 180° = 135°

Final Answer

The angle of inclination for a line with the slope of -1 is either -45° or 135°.