Question

2. Write a linear inequality in two variables that has the following two properties. Explain how you know

Answer 1

We are asked to determine an inequality that does not contain the following points as solutions:

$(0,0);(0,-1);(0,1)$

And the following are solutions:

$(1,1);(3,-1);(-1,3)$

First, we will plot the points:

Therefore, we can use a line that has y-intercept 2 and x-intercept 2, like this:

To determine the equation of the line we use the intercept form of a line equation:

$\frac{x}{a}+\frac{y}{b}=1$

Where:

$\begin{gathered} a=\text{ x-intercept} \\ b=\text{ y-intercept} \end{gathered}$

Now, we substitute the intercepts:

$\frac{x}{2}+\frac{y}{2}=1$

Now, we multiply both sides by 2:

$x+y=2$

Now, we subtract "x" from both sides:

$y=2-x$

Now, since the points are included in the line and we need the solutions to be above the line we use the inequality sign "greater or equal to":

$y\ge2-x$

The graph is the following:

Thus we get the required inequality.