Calculation:

Consider, the equation, \(\displaystyle{4}{x}—{5}{y}={12}\),

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

\(\displaystyle{4}{x}-{5}\cdot{0}={12}\)

\(\displaystyle{4}{x}={12}\)

Divide both sides by 4,

\(\displaystyle{\frac{{{4}{x}}}{{{4}}}}={\frac{{{12}}}{{{4}}}}\)

\(\displaystyle{x}={3}\)

So, the x-intercept is (3, 0).

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

\(\displaystyle{4}\cdot{0}-{5}{y}={12}\)

\(\displaystyle-{5}{y}={12}\)

Divide both sides of the equation by —5,

\(\displaystyle{\frac{{-{5}{y}}}{{-{5}}}}={\frac{{{12}}}{{-{5}}}}\)

\(\displaystyle{y}={\frac{{-{12}}}{{{5}}}}\)

So, the y-intercept is \(\displaystyle{\left({0},{\frac{{-{12}}}{{{5}}}}\right)}\).

Hence, the x and y-intercepts of \(\displaystyle{4}{x}-{5}{y}={12}\) are (3,0) and \(\displaystyle{\left({0},{\frac{{-{12}}}{{{5}}}}\right)}\), respectively.

Consider, the equation, \(\displaystyle{4}{x}—{5}{y}={12}\),

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

\(\displaystyle{4}{x}-{5}\cdot{0}={12}\)

\(\displaystyle{4}{x}={12}\)

Divide both sides by 4,

\(\displaystyle{\frac{{{4}{x}}}{{{4}}}}={\frac{{{12}}}{{{4}}}}\)

\(\displaystyle{x}={3}\)

So, the x-intercept is (3, 0).

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

\(\displaystyle{4}\cdot{0}-{5}{y}={12}\)

\(\displaystyle-{5}{y}={12}\)

Divide both sides of the equation by —5,

\(\displaystyle{\frac{{-{5}{y}}}{{-{5}}}}={\frac{{{12}}}{{-{5}}}}\)

\(\displaystyle{y}={\frac{{-{12}}}{{{5}}}}\)

So, the y-intercept is \(\displaystyle{\left({0},{\frac{{-{12}}}{{{5}}}}\right)}\).

Hence, the x and y-intercepts of \(\displaystyle{4}{x}-{5}{y}={12}\) are (3,0) and \(\displaystyle{\left({0},{\frac{{-{12}}}{{{5}}}}\right)}\), respectively.