# Find the x-and y-intercepts of the graph of the equation algebraically. 3y+2.5x-3.4=0

Upper level algebra
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{3}{y}+{2.5}{x}-{3.4}={0}$$

2020-11-09
Calculation:
Consider, the equation, $$\displaystyle{3}{y}+{2.5}{x}—{3.4}={0}$$,
To compute x-intercept, put $$\displaystyle{y}={0}$$,
$$\displaystyle{3}\cdot{0}+{2.5}{x}-{3.4}={0}$$
$$\displaystyle{2.5}{x}-{3.4}+{3.4}={0}+{3.4}$$
$$\displaystyle{\frac{{{2.5}}}{{{2.5}}}}{x}={\frac{{{3.4}}}{{{2.5}}}}$$
$$\displaystyle{x}={1.36}$$
So, the x-intercept is (1.36, 0).
To compute y -intercept, put $$\displaystyle{x}={0}$$,
$$\displaystyle{3}{y}+{2.5}\times{0}-{3.4}={0}$$
$$\displaystyle{\frac{{{3}{y}}}{{{3}}}}={\frac{{{3.4}}}{{{3}}}}$$
$$\displaystyle{y}={\frac{{{3.4}}}{{{3}}}}$$
$$\displaystyle{y}={1.13}$$
So, the y -intercept is (0, 1.13).
Hence, the x and y-intercepts of $$\displaystyle{3}{y}+{2.5}{x}-{3.4}={0}$$ are (1.36,0) and (0,1.13), respectively.