# Consider the differential equation dy/dx= (y-1)/x. On the axes, sketch a slope field for the given differential equation at the nine points indicated.

**Solution:**

Lets first construct a table which contains the values of slope y’ = dydx = (y - 1)/x for 1 ≤ x ≤ 3, 0 ≤ y ≤ 2

For example when x = 1 and y = 0 then slope -1 which is the cell(1,1) of the table below. When x = 1 and y The cells contain the value of the slope for various values of x and y. The limits of x and y have already been given above.

x/y | 0 | 1 | 2 |

1 | -1 | 0 | 1 |

2 | -1/2 | 0 | 1/2 |

3 | -1/3 | 0 | 1/3 |

These values of the slope are now plotted on an x-y plane which is called a slope field. Basically, slope fields are plotting small line segments of the slopes contained in the table above. The graph of the plot is given below:

Also, note that for y = 1 the slope of all the line segments is zero and that is why they are flat lines. The lowest level segments have negative slopes.

## Consider the differential equation dy/dx= (y - 1)/x. On the axes, sketch a slope field for the given differential equation at the nine points indicated.

**Summary:**

The differential equation dy/dx= (y - 1)/x is plotted below on a graph which is basically called a slope field.

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