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

Question
Upper level algebra
asked 2020-11-22
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}$$

## Answers (1)

2020-11-23
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 $$\displaystyle{\left({0},{\frac{{{2}}}{{{3}}}}\right)}$$.

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