Calculation:

Consider, the equation,

\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)

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

\(\displaystyle{0}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)

\(\displaystyle{\frac{{{1}}}{{{2}}}}{x}={\frac{{{2}}}{{{3}}}}\)

\(\displaystyle{x}={\frac{{{2}}}{{{3}}}}\times{2}\)

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

Therefore, the x -intercept is \(\displaystyle{\left({\frac{{{4}}}{{{3}}}},{0}\right)}\).

To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\),

\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}\times{0}+{\frac{{{2}}}{{{3}}}}\)

\(\displaystyle={\frac{{{2}}}{{{3}}}}\)

Therefore, y -intercept is \(\displaystyle{\left({0},{\frac{{{2}}}{{{3}}}}\right)}\).

Consider, the equation,

\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)

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

\(\displaystyle{0}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)

\(\displaystyle{\frac{{{1}}}{{{2}}}}{x}={\frac{{{2}}}{{{3}}}}\)

\(\displaystyle{x}={\frac{{{2}}}{{{3}}}}\times{2}\)

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

Therefore, the x -intercept is \(\displaystyle{\left({\frac{{{4}}}{{{3}}}},{0}\right)}\).

To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\),

\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}\times{0}+{\frac{{{2}}}{{{3}}}}\)

\(\displaystyle={\frac{{{2}}}{{{3}}}}\)

Therefore, y -intercept is \(\displaystyle{\left({0},{\frac{{{2}}}{{{3}}}}\right)}\).