For, x-intercept, \(\displaystyle{y}={0}\):

\(\displaystyle\Rightarrow{0}={14}{x}-{6}\)

\(\displaystyle\Rightarrow{6}={14}{x}\)

\(\displaystyle\Rightarrow{14}{x}={6}\)

\(\displaystyle\Rightarrow{x}={\frac{{{6}}}{{{14}}}}\)

\(\displaystyle\Rightarrow{x}={\frac{{{3}}}{{{7}}}}\)

So, x-intercept \(\displaystyle={\left({\frac{{{3}}}{{{7}}}},{0}\right)}\)

For, y-intercept, \(\displaystyle{x}={0}\):

\(\displaystyle\Rightarrow{y}={14}{\left({0}\right)}-{6}\)

\(\displaystyle\Rightarrow{y}={0}-{6}\)

\(\displaystyle\Rightarrow{y}=-{6}\)

so, y-intercept=(0,-6)

\(\displaystyle\Rightarrow{0}={14}{x}-{6}\)

\(\displaystyle\Rightarrow{6}={14}{x}\)

\(\displaystyle\Rightarrow{14}{x}={6}\)

\(\displaystyle\Rightarrow{x}={\frac{{{6}}}{{{14}}}}\)

\(\displaystyle\Rightarrow{x}={\frac{{{3}}}{{{7}}}}\)

So, x-intercept \(\displaystyle={\left({\frac{{{3}}}{{{7}}}},{0}\right)}\)

For, y-intercept, \(\displaystyle{x}={0}\):

\(\displaystyle\Rightarrow{y}={14}{\left({0}\right)}-{6}\)

\(\displaystyle\Rightarrow{y}={0}-{6}\)

\(\displaystyle\Rightarrow{y}=-{6}\)

so, y-intercept=(0,-6)