Question

Who is the best portion of the west to the all theA

Answer 1

The inequality given is:

`x+y\le5`

In order to graph this inequality, we need two points that will show us where the line (x+y = 5) is.

The easiest points to get are the values of x and y when the other is zero i.e.

The value of x when y = 0 to give (x, 0) as one point and

The value of y when x = 0 to give (0, y) as the second point.

This is done below:

`\begin{gathered} x+y=5 \\ \text{when,} \\ x=0 \\ 0+y=5 \\ \therefore y=5 \\ The\text{ point is: (0, 5)} \\ \\ x+y=5 \\ \text{when,} \\ y=0 \\ x+0=5 \\ \therefore x=5 \\ \text{The point is: (5, 0)} \end{gathered}`

So now we have two points: (0, 5) and (5, 0)

Also in order to plot these points for the inequality, we need to know which part of the graph should be discarded.

We will also use these two points but this time, with the inequality sign.

`\begin{gathered} x=5,\text{ when y = 0} \\ \text{This becomes} \\ x\le5 \\ \text{This means that all parts of the graph where x is less than or equal} \\ to\text{ 5 is a valid region and all other parts are to be discarded.} \\ \\ y=5,\text{ when x= 0} \\ \text{This becomes} \\ y\le5 \\ \text{This means that all parts of the graph where y is less than or equal} \\ to\text{ 5 is valid and all other parts are to be discarded} \end{gathered}`

Because the inequality is less than or equal to, we must make the line solid instead of dashed

Now let us sketch this inequality:

Comparing this with the options,

The final answer is: Option D