# A question on Multiple RegionPlots

I want to find the output of RegionPlot for a simple condition namely n*(x + y) < 1, where n is a varying number.

Here I have used Manipulate command in order to generate multiple RegionPlots (with different areas) for varying n values.

Manipulate[RegionPlot[{nx + ny < 1}, {x, -1, 1}, {y, -1, 1}], {n, 1, 10, 0.1}]

Now I want to generate a single region whose area changes with n for all values n=1..10, and also its color (or color intensity) varies as n changes.

So for example, as n decreases the intensity of the color decreases and this intensity is shown as a Legend near the diagram.

Can anyone help me with this issue?

Thank you so much.

Clear["Global*"]

Manipulate[
RegionPlot[{n*x + n*y < 1}, {x, -1, 1}, {y, -1, 1},
PlotStyle -> ColorData["Rainbow"][Rescale[n, {1, 10}]]], {{n, 5}, 1,
10, 0.1, Appearance -> "Labeled"}] Legended[
Show[
RegionPlot[
{#*x + #*y < 1}, {x, -1, 1}, {y, -1, 1},
PlotStyle -> ColorData["Rainbow"][Rescale[#, {1, 10}]],
PlotPoints -> 75,
MaxRecursion -> 5] & /@ Range],
SwatchLegend[
ColorData["Rainbow"][Rescale[#, {1, 10}]] & /@ Range,
Range]] • Thank you Bob, is it possible to make the jumps between colors continues so that the change in color occurs more smoothly? – user14750 Apr 15 at 22:26

To get the continues effect I think we need to use ColorFunction,here we try the LinearGradientFilling .

normal = {1, 1};
Manipulate[
Region[Style[ImplicitRegion[n*normal . {x, y} < 1, {x, y}],
`