the assumption being that "x" is a plain variable whilst "y" is a function, that matters because the chain rule would be needed for a function, not so for a plain variable.

$4x^2+4x+xy=5\implies 8x+4+\stackrel{\textit{product rule}}{\left( 1\cdot y+x\cdot \cfrac{dy}{dx} \right)}=0 \\\\\\ x\cfrac{dy}{dx}=-8x-4-y\implies \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x}$

now, we know that y(5) = -23, which is another way of saying that when x = 5, y = -23, but we already knew that, we can get that by simply plugging it into the equation hmmm y'(5), well

$\left. \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x} \right|_{\stackrel{x=5~}{\textit{\tiny y=-23}}}\implies \cfrac{-8(5)-4-(-23)}{5}\implies \cfrac{-21}{5}$

8 0

2 years ago

Graph the line.<br> y + 4x=8

const2013 [10]

Y-Intercept =(−8)
Go to the graph and plot the point the point (0,−8) on the y-axis.
Then rise 4 and run 1. Plot the point (1,−4)
Then again "rise 4" and then "run" 1. Plot the point (2,0)

6 0

2 years ago

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