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Nikhil Sinha · Answer 1 · 2018-12-11T10:41:23+0000

the slope of a line who is perpendicular to another, is the negative reciprocal slope of that line, that is, if a line has slope say a/b, then

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\ slope=-2\qquad negative\implies +2\qquad reciprocal\implies \cfrac{1}{2}$

so.. what is the equation of a line whose slope is 1/2 and passes through (2,5)?

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ 5}})\quad \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{1}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{1}{2}(x-2)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-5=\cfrac{1}{2}x-1\implies y=\cfrac{1}{2}x+4$

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