Consider the slope field for the differential equation

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

\dfrac{dy}{dx}=y-x

. Which of the following correctly compares the steepness of the solution curve through

(2,3)

with that of the solution curve through

(0,0)

at those respective points? (a) The curve through

(0,0)

is steeper because its slope is larger than that at

(2,3)

. (b) Both curves have the same steepness because their slopes at those points are equal. (c) The curve through

(2,3)

is steeper because its slope is larger than that at

(0,0)

. (d) Neither curve is steep because the slopes at both points are zero.