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 \(\displaystyle{\left({0},{\frac{{{2}}}{{{3}}}}\right)}\).
0

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