Calculation:

Consider, the equation, \(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}—{2}{y}={0}\),

To compute x-intercept, put \(\displaystyle{y}={0}\),

\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}—{2}\cdot{0}={0}\)

\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}-{5}={0}-{5}\)

\(\displaystyle{\frac{{{3}}}{{{8}}}}\cdot{\frac{{{8}{x}}}{{{3}}}}={\frac{{{3}}}{{{8}}}}\cdot{\left(-{5}\right)}\)

\(\displaystyle{x}={\frac{{-{15}}}{{{8}}}}\)

So, the x-intercept is \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\).

To compute y -intercept, put \(\displaystyle{x}={0}\),

\(\displaystyle{\frac{{{8}\cdot{0}}}{{{3}}}}+{5}-{2}{y}={0}\)

\(\displaystyle{5}-{2}{y}-{5}={0}-{5}\)

\(\displaystyle{\frac{{-{2}}}{{-{2}}}}{y}={\frac{{-{5}}}{{{2}}}}\)

\(\displaystyle{y}={\frac{{-{5}}}{{-{2}}}}\)

So, the y-intercept is \(\displaystyle{\left({0},{\frac{{{5}}}{{{2}}}}\right)}\).

Hence, the x and y -intercepts of \(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}-{2}{y}={0}\) are \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\) and \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\) and \(\displaystyle{\left({0},{\frac{{{5}}}{{{2}}}}\right)}\),respectively.

Consider, the equation, \(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}—{2}{y}={0}\),

To compute x-intercept, put \(\displaystyle{y}={0}\),

\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}—{2}\cdot{0}={0}\)

\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}-{5}={0}-{5}\)

\(\displaystyle{\frac{{{3}}}{{{8}}}}\cdot{\frac{{{8}{x}}}{{{3}}}}={\frac{{{3}}}{{{8}}}}\cdot{\left(-{5}\right)}\)

\(\displaystyle{x}={\frac{{-{15}}}{{{8}}}}\)

So, the x-intercept is \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\).

To compute y -intercept, put \(\displaystyle{x}={0}\),

\(\displaystyle{\frac{{{8}\cdot{0}}}{{{3}}}}+{5}-{2}{y}={0}\)

\(\displaystyle{5}-{2}{y}-{5}={0}-{5}\)

\(\displaystyle{\frac{{-{2}}}{{-{2}}}}{y}={\frac{{-{5}}}{{{2}}}}\)

\(\displaystyle{y}={\frac{{-{5}}}{{-{2}}}}\)

So, the y-intercept is \(\displaystyle{\left({0},{\frac{{{5}}}{{{2}}}}\right)}\).

Hence, the x and y -intercepts of \(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}-{2}{y}={0}\) are \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\) and \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\) and \(\displaystyle{\left({0},{\frac{{{5}}}{{{2}}}}\right)}\),respectively.