Answer:
The graph is shown below.
Step-by-step explanation:
Given:
The inequality of a line to graph is given as:
[tex]y<x-3[/tex]
In order to graph it, we first make the 'inequality' sign to 'equal to' sign. This gives,
[tex]y=x-3[/tex]
Now, we plot this line on a graph. The given line is of the form:
[tex]y=mx+b[/tex] Where, 'm' is the slope and 'b' is the y-intercept.
So, for the line [tex]y=x-3[/tex], [tex]m=1,b=-3[/tex]
The y-intercept is at (0, -3).
In order to draw the line correctly we find another point. Let the 'y' value be 0.
Now, [tex]0=x-3\\x=3[/tex]
So, the point is (3, 0).
Now, we mark these points and draw a line passing through these two points.
Now, consider the line inequality [tex]y<x-3[/tex]. The 'y' value is less than [tex]x-3[/tex]. So, the solution region will be region below the line and excluding all the points on the line. So, we draw a broken line and shade the region below it.
The graph is shown below.
