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Anit [1.1K]
4 years ago
14

Write an equation that is perpendicular to y= 1/2x+5 and passes through (4,8)

Mathematics
1 answer:
goblinko [34]4 years ago
4 0

Answer:

y = -2x + 16.

Step-by-step explanation:

The slope of the perpendicular line = -1 / slope of the given line

= -1 / 1/2 = -2.

Using the point slope form of the equation of a straight line:

y - y1 = m (x - x1)

y - 8 = -2(x - 4)

y - 8 = -2x + 8

y = -2x + 16  is the required equation.

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\bf \begin{array}{lccclll}
&\stackrel{gallons}{amount}&\stackrel{\%}{quantity}&\stackrel{antifreeze}{quantity}\\
&------&------&------\\
\textit{80\% sol'n}&x&0.80&0.8x\\
\textit{10\% sol'n}&100&0.10&10\\
------&------&------&------\\
mixture&y&0.70&0.7y
\end{array}

so whatever "x" is, we know that x + 100 = y.

and we know that 0.8x + 10 = 0.7y.

\bf \begin{cases}
x+100=\boxed{y}\\
0.8x+10=0.7y\\
----------\\
0.8x+10=0.7\left( \boxed{x+100} \right)
\end{cases}
\\\\\\
0.8x+10=0.7x+70\implies 0.8x-0.7x=70-10\implies 0.1x=60
\\\\\\
x=\cfrac{60}{0.1}\implies x=600
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