Question

Graph the inequality x-2y less than or equal to 0

Answer 1

To graph the inequality, we can do the following steps.

Step 1: We rearrange the equation so y is on the left and everything else is on the right.

`\begin{gathered} x-2y\le0 \\ \text{ Subtract x from both sides} \\ x-2y-x\le0-x \\ -2y\le-x \\ \text{ Divide by -2 from both sides} \\ (-2y)/(-2)\le(-x)/(-2) \\ y\ge(x)/(2) \end{gathered}`

Step 2: We plot the line associated with the inequality. For this, we choose two values of x and replace them in the below equation.

`\begin{gathered} x=2 \\ $$\boldsymbol{y=(x)/(2)}$$ \\ y=(2)/(2) \\ y=1 \\ \text{ Then, the lines passes through the point (2,1).} \end{gathered}`
`\begin{gathered} x=4 \\ y=(x)/(2) \\ y=(4)/(2) \\ y=2 \\ \text{ Then, the lines passes through the point (4,2).} \end{gathered}`

Since inequality has the symbol ≥, we make a solid line.

Step 3: Since inequality has the symbol ≥, we shade above the line. Therefore, the graph of the inequality is: