Find the x-and y-intercepts of the graph of the equation algebraically. y=2x+3y=10

Question
Upper level algebra
asked 2020-12-02
Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{y}={2}{x}+{3}{y}={10}\)

Answers (1)

2020-12-03
Calculation:
Consider, the equation \(\displaystyle{2}{x}+{3}{y}={10}\),
To compute x-intercept, put \(\displaystyle{y}={0}\).
\(\displaystyle{2}{x}+{3}\cdot{0}={10}\)
\(\displaystyle{2}{x}={10}\)
Divide both sides of the equation,
\(\displaystyle{\frac{{{2}{x}}}{{{2}}}}={\frac{{{10}}}{{{2}}}}\)
\(\displaystyle{x}={5}\)
So, the x-intercept is \(\displaystyle{\left({5},{0}\right)}\).
To compute y-intercept, put \(\displaystyle{x}={0}\),
\(\displaystyle{2}\cdot{0}+{3}{y}={10}\)
\(\displaystyle{3}{y}={10}\)
Divide both sides of the equation by 3,
\(\displaystyle{\frac{{{3}{y}}}{{{3}}}}={\frac{{{10}}}{{{3}}}}\)
\(\displaystyle{y}={\frac{{{10}}}{{{3}}}}\)
So, the y -intercept is \(\displaystyle{\left({0},{\frac{{{10}}}{{{3}}}}\right)}\).
Hence, the x and y -intercept of \(\displaystyle{2}{x}+{3}{y}={10}\) are \(\displaystyle{\left({5},{0}\right)}\) and \(\displaystyle{\left({0},{\frac{{{10}}}{{{3}}}}\right)}\), respectively.
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