Use implicit differentiation to find $d y / d x$ . Then find the slope of the curve at the given point.
$5 x y - 8 x + y = 40; (- 4, - \frac{8}{19})$
$\frac{d y}{d x} = \frac{8 - 5 y}{5 x + 1}$
The slope of the curve at $(- 4, - \frac{8}{19})$ is $◻$ .

Answer

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Answer

Final Answer: The slope of the curve at $(- 4, - \frac{8}{19})$ is $- 0.531855955678670$ .

Steps

Step 1 ：Use implicit differentiation to find $\frac{d y}{d x}$ .

Step 2 ： $\frac{d y}{d x} = \frac{8 - 5 y}{5 x + 1}$

Step 3 ：Substitute the x and y coordinates of the given point into the derivative to find the slope at that point.

Step 4 ： $\frac{d y}{d x} = \frac{8 - 5 * (- \frac{8}{19})}{5 * (- 4) + 1}$

Step 5 ：Simplify the expression to find the slope.

Step 6 ：The slope of the curve at $(- 4, - \frac{8}{19})$ is $- 0.531855955678670$ .

Step 7 ：Final Answer: The slope of the curve at $(- 4, - \frac{8}{19})$ is $- 0.531855955678670$ .