Question

Find the x-and y-intercepts of the graph of the equation algebraically.
\(\displaystyle{y}=-{5}{x}+{6}\)

Answer 1

Calculation:
Consider, the equation,
\(\displaystyle{y}=-{5}{x}+{6}\)
To determine x-intercept, substitute \(\displaystyle{y}={0}\) in the above equation,
\(\displaystyle{0}=-{5}{x}+{6}\)
\(\displaystyle{5}{x}={6}\)
\(\displaystyle{x}={\frac{{{6}}}{{{5}}}}\)
Therefore, the x-intercept is \(\displaystyle{\left({\frac{{{6}}}{{{5}}}},{0}\right)}\).
To determine y -intercept, substitute \(\displaystyle{x}={0}\) in the equation, \(\displaystyle{y}=-{5}{x}+{6}\),
\(\displaystyle{y}=-{5}\times{0}+{6}={6}\)
Therefore, y-intercept is \(\displaystyle{\left({0},{6}\right)}\).