Find the x-and y-intercepts of the graph of the equation algebraically. \frac{8x}{3}+50-2y=0

Find the x-and y-intercepts of the graph of the equation algebraically. \frac{8x}{3}+50-2y=0

Question
Upper level algebra
asked 2021-03-06
Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{50}-{2}{y}={0}\)

Answers (1)

2021-03-07
Calculation:
Consider, the equation, \(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}—{2}{y}={0}\),
To compute x-intercept, put \(\displaystyle{y}={0}\),
\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}—{2}\cdot{0}={0}\)
\(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}-{5}={0}-{5}\)
\(\displaystyle{\frac{{{3}}}{{{8}}}}\cdot{\frac{{{8}{x}}}{{{3}}}}={\frac{{{3}}}{{{8}}}}\cdot{\left(-{5}\right)}\)
\(\displaystyle{x}={\frac{{-{15}}}{{{8}}}}\)
So, the x-intercept is \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\).
To compute y -intercept, put \(\displaystyle{x}={0}\),
\(\displaystyle{\frac{{{8}\cdot{0}}}{{{3}}}}+{5}-{2}{y}={0}\)
\(\displaystyle{5}-{2}{y}-{5}={0}-{5}\)
\(\displaystyle{\frac{{-{2}}}{{-{2}}}}{y}={\frac{{-{5}}}{{{2}}}}\)
\(\displaystyle{y}={\frac{{-{5}}}{{-{2}}}}\)
So, the y-intercept is \(\displaystyle{\left({0},{\frac{{{5}}}{{{2}}}}\right)}\).
Hence, the x and y -intercepts of \(\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{5}-{2}{y}={0}\) are \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\) and \(\displaystyle{\left({\frac{{-{15}}}{{{8}}}},{0}\right)}\) and \(\displaystyle{\left({0},{\frac{{{5}}}{{{2}}}}\right)}\),respectively.
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