Question

The $x$ and $y$ intercepts of the following line is:

$3x+y-\frac{5}{3}=0$

• A. $x-intercept=a=\frac{9}{5}y-intercept=b=\frac{3}{5}$
• B. $x-intercept=a=\frac{5}{9}y-intercept=b=\frac{5}{3}$
• C. $x-intercept=a=\frac{5}{9}y-intercept=b=\frac{-5}{3}$
• D. $x-intercept=a=\frac{9}{5}y-intercept=b=\frac{-3}{5}$

Answer 1

The correct option is C $x-intercept=a=\frac{5}{9}y-intercept=b=\frac{-5}{3}$

$Given-theequationofalineis3x+y-\frac{5}{3}=0.Tofindout-theequationofthelineininterceptformwhichis\frac{x}{a}+\frac{y}{b}=1whena=x-interceptandb=y-intercept.Solution-3x+y-\frac{5}{3}=0⟹3x+y=\frac{5}{3}⟹9x+3y=5Dividingbothsidesby5weget\frac{9x}{5}+\frac{3y}{5}=1⟹\frac{x}{\frac{5}{9}}+\frac{y}{\frac{5}{3}}=1.\therefore x-intercept=a=\frac{5}{9}y-intercept=b=\frac{5}{3}.Ans-OptionC.$