Calculation:

Consider, the equation,

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

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

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

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

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

Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{1}}}{{{3}}}},{0}\right)}\).

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

\(\displaystyle{y}={3}{\left({0}\right)}-{1}\)

\(\displaystyle={0}-{1}=-{1}\)

Therefore, y -intercept is (0, -1).

Consider, the equation,

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

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

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

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

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

Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{1}}}{{{3}}}},{0}\right)}\).

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

\(\displaystyle{y}={3}{\left({0}\right)}-{1}\)

\(\displaystyle={0}-{1}=-{1}\)

Therefore, y -intercept is (0, -1).