# Find the x-and y-intercepts of the graph of the equation algebraically. 4x-5y=12

Upper level algebra
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{4}{x}-{5}{y}={12}$$

2020-10-19
Calculation:
Consider, the equation, $$\displaystyle{4}{x}—{5}{y}={12}$$,
To compute x-intercept, put $$\displaystyle{y}={0}$$,
$$\displaystyle{4}{x}-{5}\cdot{0}={12}$$
$$\displaystyle{4}{x}={12}$$
Divide both sides by 4,
$$\displaystyle{\frac{{{4}{x}}}{{{4}}}}={\frac{{{12}}}{{{4}}}}$$
$$\displaystyle{x}={3}$$
So, the x-intercept is (3, 0).
To compute y -intercept, put $$\displaystyle{x}={0}$$,
$$\displaystyle{4}\cdot{0}-{5}{y}={12}$$
$$\displaystyle-{5}{y}={12}$$
Divide both sides of the equation by —5,
$$\displaystyle{\frac{{-{5}{y}}}{{-{5}}}}={\frac{{{12}}}{{-{5}}}}$$
$$\displaystyle{y}={\frac{{-{12}}}{{{5}}}}$$
So, the y-intercept is $$\displaystyle{\left({0},{\frac{{-{12}}}{{{5}}}}\right)}$$.
Hence, the x and y-intercepts of $$\displaystyle{4}{x}-{5}{y}={12}$$ are (3,0) and $$\displaystyle{\left({0},{\frac{{-{12}}}{{{5}}}}\right)}$$, respectively.