Question

If $4x - 7y + 15 = 0$ then derivative of $y$ with respect to $x$ is

• A. $-4/7$
• B. $0$
• C. $4$
• D. $4/7$

Hint:

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, $-\frac{4}{-7} = \frac{4}{7}$.

Answer 1

The Correct Option is D

To find the derivative $\frac{dy}{dx}$, we can use implicit differentiation or rearrange the equation into the slope-intercept form ($y = mx + c$). 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.