Which slope field is generated by the differential equation
$$
\frac{d y}{d x}=\frac{x-2}{y} \text { ? }
$$

Choose 1 answer:
(A)
(B)
(C)
(D)
(E)

Question

Which slope field is generated by the differential equation
$$
\frac{d y}{d x}=\frac{x-2}{y} \text { ? }
$$

Choose 1 answer:
(A)
(B)
(C)
(D)
(E)

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ The given differential equation is $\frac{d y}{d x} = \frac{x-2}{y}$. ‖ ‖ step 2 ⋮ To determine the correct slope field, we need to analyze the behavior of the slopes based on the equation $\frac{d y}{d x} = \frac{x-2}{y}$. ‖ ‖ step 3 ⋮ For $x > 2$, $\frac{x-2}{y}$ is positive if $y > 0$ and negative if $y < 0$. ‖ ‖ step 4 ⋮ For $x < 2$, $\frac{x-2}{y}$ is negative if $y > 0$ and positive if $y < 0$. ‖ ‖ step 5 ⋮ At $x = 2$, $\frac{d y}{d x} = 0$ for all $y$. ‖ ‖ step 6 ⋮ Based on these observations, the slopes are positive in the first and third quadrants and negative in the second and fourth quadrants. ‖ ‖ step 7 ⋮ The slopes appear to be steeper as the absolute value of $x$ increases. ‖ ***A*** ∻Key Concept∻ ⚹Slope Field Analysis⚹ ∻Explanation∻ ⚹The slope field of a differential equation $\frac{d y}{d x} = \frac{x-2}{y}$ shows the behavior of the slopes based on the values of $x$ and $y$. By analyzing the signs and steepness of the slopes in different quadrants, we can match the correct graph.⚹◊What is the relationship between the slopes of the line segments in the graphs and the values of x in the given slope field differential equation⍭ Generate me a similar question◊

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