Calculation:

Consider, the equation \(\displaystyle{2}{x}+{3}{y}={10}\),

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

\(\displaystyle{2}{x}+{3}\cdot{0}={10}\)

\(\displaystyle{2}{x}={10}\)

Divide both sides of the equation,

\(\displaystyle{\frac{{{2}{x}}}{{{2}}}}={\frac{{{10}}}{{{2}}}}\)

\(\displaystyle{x}={5}\)

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

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

\(\displaystyle{2}\cdot{0}+{3}{y}={10}\)

\(\displaystyle{3}{y}={10}\)

Divide both sides of the equation by 3,

\(\displaystyle{\frac{{{3}{y}}}{{{3}}}}={\frac{{{10}}}{{{3}}}}\)

\(\displaystyle{y}={\frac{{{10}}}{{{3}}}}\)

So, the y -intercept is \(\displaystyle{\left({0},{\frac{{{10}}}{{{3}}}}\right)}\).

Hence, the x and y -intercept of \(\displaystyle{2}{x}+{3}{y}={10}\) are \(\displaystyle{\left({5},{0}\right)}\) and \(\displaystyle{\left({0},{\frac{{{10}}}{{{3}}}}\right)}\), respectively.

Consider, the equation \(\displaystyle{2}{x}+{3}{y}={10}\),

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

\(\displaystyle{2}{x}+{3}\cdot{0}={10}\)

\(\displaystyle{2}{x}={10}\)

Divide both sides of the equation,

\(\displaystyle{\frac{{{2}{x}}}{{{2}}}}={\frac{{{10}}}{{{2}}}}\)

\(\displaystyle{x}={5}\)

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

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

\(\displaystyle{2}\cdot{0}+{3}{y}={10}\)

\(\displaystyle{3}{y}={10}\)

Divide both sides of the equation by 3,

\(\displaystyle{\frac{{{3}{y}}}{{{3}}}}={\frac{{{10}}}{{{3}}}}\)

\(\displaystyle{y}={\frac{{{10}}}{{{3}}}}\)

So, the y -intercept is \(\displaystyle{\left({0},{\frac{{{10}}}{{{3}}}}\right)}\).

Hence, the x and y -intercept of \(\displaystyle{2}{x}+{3}{y}={10}\) are \(\displaystyle{\left({5},{0}\right)}\) and \(\displaystyle{\left({0},{\frac{{{10}}}{{{3}}}}\right)}\), respectively.