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

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

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.

Relevant Questions

Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{\frac{{{2}{x}}}{{{5}}}}+{8}-{3}{y}={0}$$
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}$$
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}$$
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{3}{y}+{2.5}{x}-{3.4}={0}$$
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}={4}{y}-{0.75}{x}+{1.2}={0}$$
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}=-{3}{\left({2}{x}+{1}\right)}$$
$$\displaystyle{y}={16}-{3}{x}$$
$$\displaystyle{4}{x}-{5}{y}={12}$$
$$\displaystyle{y}={5}-{\left({6}-{x}\right)}$$
$$\displaystyle{y}={2}{x}+{3}{y}={10}$$