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

a2linetagadaW 2020-10-18 Answered
Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{4}{x}-{5}{y}={12}\)

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Expert Answer

Adnaan Franks
Answered 2020-10-19 Author has 6853 answers
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.
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