Three slope fields (I, II, III) and three differential equations (p

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

Problem

Three slope fields (I, II, III) and three differential equations (p, q, r) are described below. Slope fields I. Slopes are constant along horizontal lines; along y=0y=0 the slope is 00, along y=1y=1 the slope is 11, and along y=2y=2 the slope is 22. II. Slopes are constant along vertical lines; along x=0x=0 the slope is −1-1, along x=1x=1 the slope is 00, and along x=2x=2 the slope is 11. III. Slopes are zero along the line y=xy=x; above that line segments tilt upward and below it they tilt downward. Differential equations p. dydx=y\dfrac{dy}{dx}=y q. dydx=x−1\dfrac{dy}{dx}=x-1 r. dydx=y−x\dfrac{dy}{dx}=y-x Which pairing of slope fields with differential equations is correct? (a) I →\to p, II →\to r, III →\to q (b) I →\to q, II →\to p, III →\to r (c) I →\to p, II →\to q, III →\to r (d) I →\to q, II →\to r, III →\to p

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