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Chapter 6: Problem 37

Find the inclination \(\theta\) (in radians and degrees) of the line. $$3 x-3 y+1=0$$

Short Answer

Expert verified
The inclination of the line is \(\pi/4\) radians or 45 degrees.

Step by step solution

01

Convert to Slope-Intercept Form

The given line is in the general form \(Ax + By + C = 0\). We convert this to the slope-intercept form \(y = mx + c\). From the equation \(3x - 3y + 1 = 0\), we first isolate \(y\). This gives us the equation of the line as: \(y = x - 1/3\).
02

Determine the Inclination in Radians

The slope, \(m\), in our equation is 1. We can find the inclination of the line in radians (\(\theta\)) using the inverse tangent or arctan of the slope \(m\), that is, \(\theta = \arctan(m) = \arctan(1) = \pi/4\) radians.
03

Convert Radians into Degrees

In order to convert radians into degrees, multiply by 180/\(\pi\). Thus, \(\theta = \pi/4 = 180/4 = 45\) degrees.

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