## Description

Here we will show how to plot the following system of linear inequalities:

(1)Sage has no inequality plotting function, so we will instead plot

(2)and use the `fill`, `fillcolor` and `fillalpha` commands to represent the inequalities manually. When graphing $x = 0$, we will instead use $y = 10^9x$ to represent a line with a vertical slope, as the normal `plot()` function cannot plot $x = 0$. Other parameters set are `ymin` and `ymax`, to prevent `fill` from poorly adjusting the viewing window, `color` to provide more easily visible borders to the regions, and `gridlines` to increase graph readability.

## Sage Cell

#### Code

```
p1 = plot(1.5 - 2*x, (x, -0.1, 1.75), ymin=-0.25, ymax=1.75, fill=10, fillcolor='cyan', color='black', fillalpha=1/3, gridlines='minor')
p2 = plot(1 - x, (x, -0.1, 1.75), ymin=-0.25, ymax=1.75, fill=10, fillcolor='magenta', color='black', fillalpha=1/3)
p3 = plot(0.5 - 0.5*x, (x, -0.1, 1.75), ymin=-0.25, ymax=1.75, fill=-10, fillcolor='yellow', color='black', fillalpha=1/3)
p4 = plot(0, (x, -0.1, 1.75), ymin=-0.25, ymax=1.75, fill=-10, fillcolor='gray', color='black', fillalpha=1/3)
p5 = plot((10^9)*x, (x, -0.1, 1.75), ymin=-0.25, ymax=1.75, fill=10, fillcolor='gray', color='black', fillalpha=1/3)
(p1 + p2 + p3 + p4 + p5).show()
```

## Options

Primary Tags: Plotting: Two-dimensional plots

Secondary Tags: Two-dimensional plots: Plotting Inequalities

## Tags

- Plotting a Circle
- Plotting a Polygon
- Plotting an Implicit Function
- Two-Dimensional Plots
- Parametric Plots
- Line Plots
- Plotting Two-Dimensional Vector Fields
- Multiple Plots on the Same Graph
- Controlling the Viewing Window of a Plot
- Plotting Functions with Asymptotes
- Multiple Annotation Techniques for Graphing
- Occasional Issues in Polar Plotting.
- Constructing Contour Plots in Sage
- Plotting Inequalities in Sage
- Plotting Nonlinear Inequalities in Sage
- Making log-log Plots in Sage

## Related Cells

Permalink:

Author: Gregory V. Bard. *Sage for Undergraduates.* American Mathematical Society, Providence, RI, 2015. Available at http://www.gregorybard.com/Sage.html.

## Attribute

Date: 02 Mar 2019 22:01

Submitted by: Zane Corbiere