Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABeasymcq1 pt

A slope field for the differential equation $\dfrac{dy}{dx} = 2$ is shown. Which of the following statements about the slope field is true?

A.All segments in the field have the same slope, and the solution curves are parallel lines.

B.The segments are horizontal, and the solution curves are horizontal lines.

C.The slopes depend on

x

but not on

y

, so the field varies from left to right.

D.The solution curves are all parabolas.

Explanation

Core Concept

With $\dfrac{dy}{dx} = 2$ the slope is constant at every point, so each solution has the form $y = 2x + C$ , a family of parallel lines.

Correct Answer

AAll segments in the field have the same slope, and the solution curves are parallel lines.

More Unit 7: Differential Equations practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 7: Differential Equations Questions →