The graph is perpendicular to the graph of 5x - y = 2 and passes through the point whose coordinates are (10,-2).

glamrockqueen7 2021-05-29 Answered
The graph is perpendicular to the graph of 5x - y = 2 and passes through the point whose coordinates are (10,-2).

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yunitsiL
Answered 2021-05-30 Author has 22954 answers

Use the point-slope form of a line: \(y-y_1=m(x-x_1)\)
where m is the slope and \((x_1\times y_1)\) is a point of the line.
Two lines are perpendicular if their slopes are negative reciprocals. Rewriting the given line, \(\displaystyle{5}{x}-{y}={2}\to{y}={5}{x}-{2}\), which has a slope of 5. So, the slope of the perpendicular line is:
\(\displaystyle{m}=-{\left(\frac{{1}}{{5}}\right)}\)
Substitute \((x_1,y_1)=(10,-2)\) so that we have: \(\displaystyle{y}-{\left(-{2}\right)}=-{\left(\frac{{1}}{{5}}\right)}{\left({x}-{10}\right)}\)
\(\displaystyle{y}+{2}=-{\left(\frac{{1}}{{5}}\right)}{x}+{2}\)
\(\displaystyle{y}=-{\left(\frac{{1}}{{5}}\right)}{x}\)

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