# Find the x-and y-intercepts of the graph of the equation algebraically. y=\frac{3}{4}x-\frac{1}{4}

Upper level algebra
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}$$

2020-11-02
Calculation:
Consider, the equation,
$$\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}$$
To determine x -intercept, substitute $$\displaystyle{y}={0}$$ in the above equation,
$$\displaystyle{0}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}$$
$$\displaystyle{\frac{{{3}}}{{{4}}}}{x}={\frac{{{1}}}{{{4}}}}$$
$$\displaystyle{x}={\frac{{{1}}}{{{4}}}}\times{\frac{{{4}}}{{{3}}}}$$
$$\displaystyle={\frac{{{1}}}{{{3}}}}$$
Therefore, the x-intercept is $$\displaystyle{\left({\frac{{{1}}}{{{3}}}},{0}\right)}$$.
To determine y -intercept, substitute $$\displaystyle{x}={0}$$ in the equation, $$\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}$$,
$$\displaystyle{y}={\frac{{{3}}}{{{4}}}}\times{0}-{\frac{{{1}}}{{{4}}}}$$
$$\displaystyle=-{\frac{{{1}}}{{{4}}}}$$
Therefore, y-intercept is $$\displaystyle{\left({0},-{\frac{{{1}}}{{{4}}}}\right)}$$.