Calculation:

Consider, the equation,

\(\displaystyle{y}=-{5}{x}+{6}\)

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

\(\displaystyle{0}=-{5}{x}+{6}\)

\(\displaystyle{5}{x}={6}\)

\(\displaystyle{x}={\frac{{{6}}}{{{5}}}}\)

Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{6}}}{{{5}}}},{0}\right)}\).

To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}=-{5}{x}+{6}\),

\(\displaystyle{y}=-{5}\times{0}+{6}={6}\)

Therefore, y-intercept is \(\displaystyle{\left({0},{6}\right)}\).

Consider, the equation,

\(\displaystyle{y}=-{5}{x}+{6}\)

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

\(\displaystyle{0}=-{5}{x}+{6}\)

\(\displaystyle{5}{x}={6}\)

\(\displaystyle{x}={\frac{{{6}}}{{{5}}}}\)

Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{6}}}{{{5}}}},{0}\right)}\).

To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}=-{5}{x}+{6}\),

\(\displaystyle{y}=-{5}\times{0}+{6}={6}\)

Therefore, y-intercept is \(\displaystyle{\left({0},{6}\right)}\).