Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - Problems - Page 32: 8

$\frac{dy}{dx}=\frac{x}{c}$

Differentiate the equation in respect to $x$, remembering to use chain rule. $$2c\frac{dy}{dx}=2x$$ Solve for the slope of the tangent line $\frac{dy}{dx}$ to get a slope of $$\frac{dy}{dx}=\frac{x}{c}$$