# The graph is perpendicular to the graph of 5x -

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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Nichole Watt

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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content_user

Answer is given below (on video)