Question

If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is

• A. $ -2 $
• B. $ -1 $
• C. $ 2 $
• D. $ 1 $
• E. $ 0 $

Answer 1

Answer: (A)

The equation of straight line passing through the points $ \left( -\frac{1}{2},1 \right) $ and (1, 2) is $ (y-{{y}_{1}})=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}(x-{{x}_{1}}) $
$ \Rightarrow $ $ (y-1)=\frac{2-1}{1+\frac{1}{2}}\left( x+\frac{1}{2} \right) $
$ \Rightarrow $ $ (y-1)=\frac{2}{3}\left( x+\frac{1}{2} \right) $
$ \Rightarrow $ $ 3(y-1)=(2x+1) $
$ \Rightarrow $ $ 2x-3y=-4 $
$ \Rightarrow $ $ \frac{x}{-2}=\frac{y}{\left( \frac{4}{3} \right)}=1 $ So, the x-intercept is $ -2 $ .