Slope Field Representation
The table shows the slopes for the differential equation $$\frac{dy}{dx}=x$$ at selected integer values of $$x$$. Which of the following describes a valid representation of the slopes for this differential equation?
| x | Slope (dy/dx) |
|---|---|
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
A
A numerical list of y-values without any reference to slopes.
B
A table listing x-values and their corresponding slopes, e.g., x = -2 gives slope -2, x = -1 gives slope -1, x = 0 gives slope 0, x = 1 gives slope 1, and x = 2 gives slope 2.
C
An equation stating $$\frac{dy}{dx}=1$$, implying constant slopes independent of x.
D
A graph of the function $$y=x^2$$, which does not depict slope information.
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