Mathematics: What is the equation of a line perpendicular to y=1/2x-1 through (0,6)

Im on the same exact question...

What is the equation of a line perpendicular to

Ответ:

natlovesfood

13.01.2022

Well, first off let's take a peek of what is the slope of "y" in this case hmmm

$\bf \begin{array}{llll}
y=&\frac{1}{2}x&-1\\
&\uparrow &~\uparrow \\
&slope&y-intercept
\end{array}$ so, is 1/2 ok....

now, a line that is perpendicular to that equation, will have a slope that is negative reciprocal of that.

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

so, what is the equation of a line whose slope is -2 and passes through (0,6)?

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 0}}\quad ,&{{ 6}})\quad 
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -2
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=-2(x-0)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-6=-2x\implies y=-2x+6$

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What is the equation of a line perpendicular to y=1/2x-1 through (0,6)

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