# 08 - Slope Fields

```Kuta Software - Infinite Calculus
Name___________________________________
Slope Fields
Date________________ Period____
Sketch the slope field for each differential equation.
dy
=x
dx
1)
2)
x
dy
=−
dx
y
y
−2
y
2
2
1.5
1.5
1
1
0.5
0.5
−1
1
2 x
−2
−1
1
−0.5
−0.5
−1
−1
−1.5
−1.5
−2
−2
2 x
For each problem, find a differential equation that could be represented with the given slope field.
3)
4)
y
−3
−2
y
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
−1
1
−0.5
1
dy
=−
dx
x
dy
C)
=1
dx
A)
2
3 x
−3
−2
−1
1
−1
−1
−1.5
−1.5
−2
−2
−2.5
−2.5
−3
−3
1
dy
=−
dx
y
dy
2
D)
=y
dx
B)
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2
−0.5
dy
=x+ y
dx
dy
C)
= xy
dx
A)
3 x
dy
=x− y
dx
dy
D)
= − xy
dx
B)
Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Slope Fields
Date________________ Period____
Sketch the slope field for each differential equation.
dy
=x
dx
1)
2)
x
dy
=−
dx
y
y
−2
y
2
2
1.5
1.5
1
1
0.5
0.5
−1
1
2 x
−2
−1
1
−0.5
−0.5
−1
−1
−1.5
−1.5
−2
−2
2 x
For each problem, find a differential equation that could be represented with the given slope field.
3)
4)
y
−3
−2
y
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
−1
1
−0.5
1
dy
=−
dx
x
dy
C)
=1
dx
A)
2
3 x
−3
−2
−1
1
−1
−1
−1.5
−1.5
−2
−2
−2.5
−2.5
−3
−3
1
dy
=−
dx
y
dy
2
*D)
=y
dx
B)
2
−0.5
dy
=x+ y
dx
dy
C)
= xy
dx
A)
3 x
dy
=x− y
dx
dy
D)
= − xy
dx
*B)
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Worksheet by Kuta Software LLC
```