Find the x-and y-intercepts of the graph of the equation algebraically. y=4y-0.75x+1.2=0

Find the x-and y-intercepts of the graph of the equation algebraically. y=4y-0.75x+1.2=0

Question
Upper level algebra
asked 2021-02-12
Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{y}={4}{y}-{0.75}{x}+{1.2}={0}\)

Answers (1)

2021-02-13
Calculation:
Consider, the equation, \(\displaystyle{4}{y}—{0.75}{x}+{1.2}={0}\),
To compute x-intercept, put \(\displaystyle{y}={0}\),
\(\displaystyle{4}\cdot{0}-{0.75}{x}+{1.2}={0}\)
\(\displaystyle{0.75}{x}+{1.2}-{1.2}={0}-{1.2}\)
\(\displaystyle{\frac{{{0.75}}}{{{0.75}}}}{x}={\frac{{{1.2}}}{{{0.75}}}}\)
\(\displaystyle{x}={1.6}\)
So, the x-intercept is \(\displaystyle{\left({1.6},{0}\right)}\).
To compute y -intercept, put \(\displaystyle{x}={0}\),
\(\displaystyle{4}{y}-{0.75}\cdot{x}+{1.2}={0}\)
\(\displaystyle{4}{y}+{1.2}-{1.2}={0}-{1.2}\)
\(\displaystyle{\frac{{{4}{y}}}{{{4}}}}={\frac{{-{1.2}}}{{{4}}}}\)
\(\displaystyle{y}=-{0.3}\)
So, the y-intercept is \(\displaystyle{\left({0},-{0.3}\right)}\).
Hence, thex and y -intercepts of \(\displaystyle{4}{y}—{0.75}{x}+{1.2}={0}\) are \(\displaystyle{\left({1.6},{0}\right)}\) and \(\displaystyle{\left({0},-{0.3}\right)}\), respectively.
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