Question

The equation of the straight lines whose inclination is pie/4 and x-intercept is 4 is

Answer 1

$\textbf{Given:}$

$\text{Angle of inclination, \theta=\dfrac{\pi}{4} }$

$\text{x-intercept=4}$

$\textbf{To find:}$

$\text{Equation of the line}$

$\textbf{Solution:}$

$\textbf{Slope of the line:}$

$m=tan\theta$

$m=tan\dfrac{\pi}{4}$

$m=1$

$\text{Equation of line in intercept form is}$

$\dfrac{x}{a}+\dfrac{y}{b}=1$

$\dfrac{x}{4}+\dfrac{y}{b}=1$

$\text{This can be written as}$

$\dfrac{y}{b}=-\dfrac{x}{4}+1$

$\implies\,y=(\dfrac{-b}{4})x+\dfrac{1}{b}$

$\text{Comparing with,}\bf\;y=mx+c$

$\dfrac{-b}{4}=m$

$\dfrac{-b}{4}=1$

$\implies\bf\,b=-4$

$\text{The required line is}$

$\dfrac{x}{4}+\dfrac{y}{-4}=1$

$\implies\bf\,x-y-4=0$

$\textbf{Answer:}$

$\textbf{Equation of the required line is \bf\,x-y-4=0 }$