Slope Fields Introduction - Grade 9 Calculus
This worksheet introduces grade 9 students to slope fields, focusing on understanding and sketching them based on given differential equations.
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Slope Fields Introduction
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Read each question carefully and follow the instructions to sketch slope fields or analyze given differential equations. Show all your work.
1. What is a slope field, and what information does it convey about a differential equation?
2. A slope field graphically represents the of the solution curves to a differential equation at various points.
3. Each small line segment in a slope field indicates the of the solution curve that passes through that point.
4. For the differential equation dy/dx = x, sketch the slope field at the indicated points on the graph below.
5. Match the following differential equations with their corresponding slope fields. (A, B, C, or D)
i) dy/dx = y
ii) dy/dx = -x/y
iii) dy/dx = x + y
iv) dy/dx = 2x
A.
B.
C.
D.
6. Consider a slope field where all the line segments along the x-axis are horizontal. What does this tell you about dy/dx when y = 0?