If $4x - 7y + 15 = 0$ then derivative of $y$ with respect to $x$ is
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For any linear equation in the form $Ax + By + C = 0$, the derivative $\frac{dy}{dx}$ (the slope) is always given by the formula $-\frac{A}{B}$. Here, $-\frac{4}{-7} = \frac{4}{7}$.
Method 1: Rearranging the Equation: Start with the given linear equation:
$$4x - 7y + 15 = 0$$
Isolate the term containing $y$:
$$-7y = -4x - 15$$
Divide the entire equation by $-7$:
$$y = \frac{-4}{-7}x - \frac{15}{-7}$$
$$y = \frac{4}{7}x + \frac{15}{7}$$
Method 2: Differentiating: Now, differentiate $y$ with respect to $x$:
$$\frac{dy}{dx} = \frac{d}{dx}\left(\frac{4}{7}x + \frac{15}{7}\right)$$
$$\frac{dy}{dx} = \frac{4}{7}$$
The derivative of a linear equation is simply the slope of the line.