Question

Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)

Answer 1

Calculation:
Consider, the equation,
\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)
To determine x -intercept, substitute \(\displaystyle{y}={0}\) in the above equation,
\(\displaystyle{0}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\)
\(\displaystyle{\frac{{{1}}}{{{2}}}}{x}={\frac{{{2}}}{{{3}}}}\)
\(\displaystyle{x}={\frac{{{2}}}{{{3}}}}\times{2}\)
\(\displaystyle={\frac{{{4}}}{{{3}}}}\)
Therefore, the x -intercept is \(\displaystyle{\left({\frac{{{4}}}{{{3}}}},{0}\right)}\).
To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}\),
\(\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}\times{0}+{\frac{{{2}}}{{{3}}}}\)
\(\displaystyle={\frac{{{2}}}{{{3}}}}\)
Therefore, y -intercept is \(\displaystyle{\left({0},{\frac{{{2}}}{{{3}}}}\right)}\).