/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 42 Find the angle of inclination of... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 42

Find the angle of inclination of the line represented by the equation. $$ 4 x-7 y-8=0 $$

Short Answer

Expert verified
The angle of inclination of the line represented by the equation \(4x-7y-8=0\) is approximately \(29.74掳\).

Step by step solution

01

Rewrite the given equation in slope-intercept form

Convert the given equation \(4x - 7y - 8 = 0\) to slope-intercept form (\(y = mx + b\)), where m is the slope, and b is the y-intercept. To do so, first isolate 'y': \(7y = 4x - 8\) Now, divide by 7 on both sides: \(y = \frac{4}{7}x - \frac{8}{7}\) Now, the line is in the slope-intercept form. Hence, we can identify the slope (m) as \(\frac{4}{7}\).
02

Calculate the angle of inclination using the slope

Since the slope is the tangent of the angle of inclination (let the angle be \(\theta\)), we can use the inverse tangent function to find the angle: \(\tan (\theta) = \frac{4}{7}\) To find \(\theta\), we use the inverse tangent function: \(\theta = \tan^{-1}( \frac{4}{7})\) Use a calculator to compute the inverse tangent: \(\theta \approx 29.74掳\)
03

Write the final answer

The angle of inclination of the line represented by the equation \(4x-7y-8=0\) is approximately \(29.74掳\).

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