For dy/dx = x - y, where on the plane is the slope <strongzero</strong?

Answer: y = x x - y = 0 \Rightarrow y = x. Slopes are zero along this line.

The slope field has constant positive slope at every point. Which differential equation does it correspond to?

Answer: dy/dx = 1 Constant slope at all points → dy/dx = constant.

A slope field has slope 1 everywhere on the line y = x and slope 0 on y = 0. The DE is likely

Answer: dy/dx = y dy/dx = y: on y = x, slope = x (not constant 1)... checking dy/dx = y: at y = 0, slope is 0 ✓. At y = 1, slope is 1. Best fit among options.

AP Calculus AB · Topic 7.3

Slope Fields Practice

Q: For dy/dx = x - y, where on the plane is the slope <strongzero</strong?

Answer: y = x x - y = 0 \Rightarrow y = x. Slopes are zero along this line.

Q: The slope field has constant positive slope at every point. Which differential equation does it correspond to?

Answer: dy/dx = 1 Constant slope at all points → dy/dx = constant.

Q: A slope field has slope 1 everywhere on the line y = x and slope 0 on y = 0. The DE is likely

Answer: dy/dx = y dy/dx = y: on y = x, slope = x (not constant 1)... checking dy/dx = y: at y = 0, slope is 0 ✓. At y = 1, slope is 1. Best fit among options.

Part of Differential Equations.(FUN-7.C)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$dy/dx = x - y$
- A
  $y = x$
  check_circle
- B
  $y = 0$
- C
  $y = -x$
- D
  $x = 0$
Why
$x - y = 0 \Rightarrow y = x$
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Sample 2difficulty 2/5
$The slope field has constant positive slope at every point. Which differential equation does it correspond to?$
- A
  $dy/dx = 0$
- B
  $dy/dx = x$
- C
  $dy/dx = y$
- D
  $dy/dx = 1$
  check_circle
Why
$dy/dx =$
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Sample 3difficulty 2/5
$1$
- A
  $dy/dx = x$
- B
  $dy/dx = x y$
- C
  $dy/dx = y$
  check_circle
- D
  $dy/dx = y - x + 1$
Why
$dy/dx = y$
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Sample 4difficulty 2/5
$A slope field shows the <strong> direction </strong> but not the speed of motion along solution curves. The slope-field segments at each point encode$
- A
  $Curvature$
- B
  $f(x, y)$
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- C
  $y$
- D
  $x$
Why
$y'$
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Sample 5difficulty 3/5
$Multiple solution curves of a slope-field DE$
- A
  $Must coincide$
- B
  $Are perpendicular to segments$
- C
  $Are always horizontal$
- D
  $Are tangent to slope-field segments at each point$
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Why
$(x, y)$
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