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

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

2020-12-26
Calculation:
Consider, the equation, $$\displaystyle{y}={12}-{5}{x}$$,
To compute x-intercept, put $$\displaystyle{y}={0}$$.
$$\displaystyle{0}={12}-{5}{x}$$
Subtract by 12, this gives,
$$\displaystyle{0}-{12}={12}-{5}{x}-{12}$$
$$\displaystyle-{12}=-{5}{x}$$
Divide the equation by -5,
$$\displaystyle{\frac{{-{5}{x}}}{{-{5}}}}={\frac{{-{12}}}{{-{5}}}}$$
$$\displaystyle{x}={\frac{{{12}}}{{{5}}}}$$
So, the x-intercept is $$\displaystyle{\left({\frac{{{12}}}{{{5}}}},{0}\right)}$$.
To compute y-intercept, put $$\displaystyle{x}={0}$$.
$$\displaystyle{y}={12}-{5}{\left({0}\right)}={12}$$
So, the y-intercept is(0,12).
Hence, the x and y-intercepts of $$\displaystyle{y}={12}-{5}{x}{\left({\frac{{{12}}}{{{5}}}},{0}\right)}$$ and(0,12),respectively.