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musickatia [10]
3 years ago
10

What is the equation of the line that is perpendicular to y=2/3x+4 and that passes through (–2,–2)?

Mathematics
1 answer:
amid [387]3 years ago
5 0
Well, <span>y=2/3x+4  is already in slope-intercept form, therefore    </span>\bf y=\stackrel{slope}{\cfrac{2}{3}}x+4.

so, a perpendicular line to a line with that slope, will have a negative reciprocal slope

\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\&#10;slope=\cfrac{2}{{{ 3}}}\qquad negative\implies  -\cfrac{2}{{{ 3}}}\qquad reciprocal\implies - \cfrac{{{ 3}}}{2}

so then, what's the equation of a line whose slope is -3/2 and goes through -2,-2?

\bf \begin{array}{lllll}&#10;&x_1&y_1\\&#10;%   (a,b)&#10;&({{ -2}}\quad ,&{{ -2}})&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{3}{2}&#10;\\\\\\&#10;% point-slope intercept&#10;\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=-\cfrac{3}{2}[x-(-2)]&#10;\\\\\\&#10;y+2=-\cfrac{3}{2}(x+2)\implies y+2=-\cfrac{3}{2}x-3\implies y=-\cfrac{3}{2}x-5
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