Find the x-and y-intercepts of the graph of the equation algebraically. y=16-3x

Question
Upper level algebra
asked 2020-11-22
Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{y}={16}-{3}{x}\)

Answers (1)

2020-11-23
Calculation:
Consider, the equation, \(\displaystyle{y}={16}—{3}{x}\),
To compute x-intercept, put \(\displaystyle{y}={0}\).
\(\displaystyle{0}={16}-{3}{x}\)
Add —16,to both the sides, this gives,
\(\displaystyle{0}-{16}={16}-{3}{x}-{16}\)
\(\displaystyle-{16}=-{3}{x}\)
Divide both sides of the equation by -3,
\(\displaystyle{\frac{{-{16}}}{{-{3}}}}={\frac{{-{3}{x}}}{{-{3}}}}\)
\(\displaystyle{x}={\frac{{{16}}}{{{3}}}}\)
So, the x-intercept is \(\displaystyle{\left({\frac{{{16}}}{{{3}}}},{0}\right)}\).
To compute y -intercept, put \(\displaystyle{x}={0}\),
\(\displaystyle{y}={16}-{3}{\left({0}\right)}\)
\(\displaystyle{y}={16}\)
So, the y-intercept is(0,16).
Hence, the x and y intercepts of \(\displaystyle{y}={16}-{3}{x}\) are \(\displaystyle{\left({\frac{{{16}}}{{{3}}}},{0}\right)}\) and(0,16),respectively.
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