Help Notes: `6x - 2y + 8 = 0` Find the inclination 'theta' (in radians and degrees) of the line.

Friday, 26 September 2014

$\displaystyle{6}{x}-{2}{y}+{8}={0}$ Find the inclination 'theta' (in radians and degrees) of the line.

Given $\displaystyle{6}{x}-{2}{y}+{8}={0}$

Find the slope of the line.

$\displaystyle{6}{x}-{2}{y}+{8}={0}$

$\displaystyle-{2}{y}=-{6}{x}-{8}$

$\displaystyle{y}={3}{x}+{4}$

The slope of the line is 3.

Find the angle of inclination.

$\displaystyle\theta={\arctan{{\left({3}\right)}}}={{71.6}}^{\circ}={1.2490}$ radians

The angle of inclination of the line whose slope is 3 is 71.6 degrees or 1.2490 radians.

Given $\displaystyle{6}{x}-{2}{y}+{8}={0}$

Find the slope of the line.

$\displaystyle{6}{x}-{2}{y}+{8}={0}$

$\displaystyle-{2}{y}=-{6}{x}-{8}$

$\displaystyle{y}={3}{x}+{4}$

The slope of the line is 3.

Find the angle of inclination.

$\displaystyle\theta={\arctan{{\left({3}\right)}}}={{71.6}}^{\circ}={1.2490}$ radians

The angle of inclination of the line whose slope is 3 is 71.6 degrees or 1.2490 radians.

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