Calculation:

Consider, the equation,

\(\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\)

To determine x -intercept, substitute \(\displaystyle{y}={0}\) in the above equation,

\(\displaystyle{0}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\)

\(\displaystyle{\frac{{{3}}}{{{4}}}}{x}={\frac{{{1}}}{{{4}}}}\)

\(\displaystyle{x}={\frac{{{1}}}{{{4}}}}\times{\frac{{{4}}}{{{3}}}}\)

\(\displaystyle={\frac{{{1}}}{{{3}}}}\)

Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{1}}}{{{3}}}},{0}\right)}\).

To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\),

\(\displaystyle{y}={\frac{{{3}}}{{{4}}}}\times{0}-{\frac{{{1}}}{{{4}}}}\)

\(\displaystyle=-{\frac{{{1}}}{{{4}}}}\)

Therefore, y-intercept is \(\displaystyle{\left({0},-{\frac{{{1}}}{{{4}}}}\right)}\).

Consider, the equation,

\(\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\)

To determine x -intercept, substitute \(\displaystyle{y}={0}\) in the above equation,

\(\displaystyle{0}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\)

\(\displaystyle{\frac{{{3}}}{{{4}}}}{x}={\frac{{{1}}}{{{4}}}}\)

\(\displaystyle{x}={\frac{{{1}}}{{{4}}}}\times{\frac{{{4}}}{{{3}}}}\)

\(\displaystyle={\frac{{{1}}}{{{3}}}}\)

Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{1}}}{{{3}}}},{0}\right)}\).

To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\),

\(\displaystyle{y}={\frac{{{3}}}{{{4}}}}\times{0}-{\frac{{{1}}}{{{4}}}}\)

\(\displaystyle=-{\frac{{{1}}}{{{4}}}}\)

Therefore, y-intercept is \(\displaystyle{\left({0},-{\frac{{{1}}}{{{4}}}}\right)}\).