Notes: `(1/4, 3/2), (1/3, 1/2)` Find the inclination 'theta' (in radians and degrees) of the line with slope m.

Wednesday, August 21, 2013

Given $\displaystyle{\left(\frac{{1}}{{4}},\frac{{3}}{{2}}\right)},{\left(\frac{{1}}{{3}},\frac{{1}}{{2}}\right)}$

Find the slope of the line passing through the two points using the formula

$\displaystyle{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}$

$\displaystyle{m}=\frac{{\frac{{1}}{{2}}-\frac{{3}}{{2}}}}{{\frac{{1}}{{3}}-\frac{{1}}{{4}}}}$ =-12

The slope of the line is -12.

Find the inclination.

$\displaystyle\theta={\arctan{{\left(-{12}\right)}}}={{94.8}}^{\circ}={1.6539}$ radians.

The inclination is 94.8 degrees or 1.6539 radians.

Notes