Write an equation of the line passing through point P (2,3) that is perpendicular to the time y-4=-2(x+3)

Mathematics

1 answer:

pshichka [43]2 years ago

3 0

Perpendicular lines have a slope that is equal to the negative inverse.
Slope is m=-2 so the new slope would be m=-(-1/2)=+1/2

Then use point slope form y-y1=m(x-x1) to get

y-2=1/2(x-3)

y=1/2x+1/2

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$\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
&& y={{ k }}x
\end{array}\\ \quad \\
$

and also

$\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
&&y=\cfrac{{{ k}}}{x}
\end{array}
$

now, we know that V varies directly to T and inversely to P simultaneously
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so $\bf V=T\cdot \cfrac{k}{P}\qquad 
\begin{cases}
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T=84\\
P=8
\end{cases}\implies 42=\cfrac{84k}{8}\implies 4=k
\\\\\\
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\begin{cases}
V=74\\
P=10
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