The family of differential equations depends on a positive parameter

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The family of differential equations

\dfrac{dy}{dx}=k y

depends on a positive parameter

k

. Describe how the slope field at any fixed point

(x,y)

changes when

k

is increased while

x

and

y

remain the same.