Question

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

Upper level algebra
ANSWERED
asked 2020-11-01
Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}\)

Answers (1)

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 \(\displaystyle{\left({0},-{\frac{{{1}}}{{{4}}}}\right)}\).
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