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Chapter 6: Problem 29

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 \(3x - 3y + 1 = 0\) is \(\pi/4\) radians or \(45^\circ\) degrees.

Step by step solution

01

Convert the given equation into slope-intercept form \(y = mx + c\)

The equation of the line can be re-arranged by making \(y\) the subject. This leads to a slope-intercept form. For the given equation, \(3x - 3y + 1 = 0\), it can be written as \(y = x - 1/3\) after dividing the equation by 3.
02

Identify the slope from the slope-intercept form

From the slope-intercept form \(y = mx + c\), the coefficient of \(x\) corresponds to slope \(m\). In this case, \(m = 1\).
03

Calculate the inclination of the line

The inclination is given by the arctangent of the slope \(m\). In radians, it can be found as \(\theta = \arctan(m) = \arctan(1) = \pi/4\). Convert this to degrees by multiplying by \(180/\pi\), which results in \(45^\circ\).

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