Question

Find the equation of the straight line which makes an angle
tan
^-1(2/3) with X-Axis

in the positive direction and Y – intercept cut off by it is 3​

Answer 1

See the photo attached for solution

Answer 2

$\underline{\textsf{Given:}}$

$\textsf{Angle of inclination of the line is}\,\mathsf{tan^{-1}(\dfrac{2}{3})}$

$\textsf{and y-intercept is 3}$

$\underline{\textsf{To find:}}$

$\textsf{The equation of the line}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the angle of inclination of the line is}\;\mathsf{\theta}$

$\implies\mathsf{\theta=tan^{-1}(\dfrac{2}{3})}$

$\implies\mathsf{tan\,\theta=\dfrac{2}{3}}$

$\implies\textsf{Slope}\mathsf{=\dfrac{2}{3}}$

$\textsf{Now}$

$\textsf{The equation of the line is}$

$\mathsf{y=mx+c}$

$\implies\mathsf{y=\dfrac{2}{3}x+3}$

$\implies\mathsf{y=\dfrac{2x+9}{3}}$

$\implies\mathsf{3y=2x+9}$

$\implies\boxed{\mathsf{2x-3y+9=0}}$

$\underline{\textsf{Answer:}}$

$\textsf{The required line is 2x-3y+9=0}$