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postnew [5]
3 years ago
15

Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line

?
Mathematics
1 answer:
Dovator [93]3 years ago
5 0

bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

now, they both intersect at 0,0, namely they both pass through it, we know the slope of the first one, so

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{1}\implies 2}}

so, we're really looking for the equation of a line whose slope is 2, and runs through (0,0).

\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=2(x-0)\implies y=2x

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Simplifying

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