91Ó°ÊÓ

Given two variable inequality is,

$y≤-\frac{1}{4}x+3$

1) First change the inequality sign to equal and draw the boundary line.

If given inequality notation is > or < then draw the boundary line is dashed.

2) Choose test point that is not on the boundary line and check test point is solution of the given inequality or not.

3) Shade one side of the boundary line.

If test point is a solution of the given inequality then shade the part include the test point.

If test point is not solution of the inequality then shade the opposite part.

We have,

$y≤-\frac{1}{4}x+3$

To draw the line first we need to change the inequality notation by equal notation.

$y=-\frac{1}{4}x+3$

Here given inequality contains the less than equal to sign it means the points on the boundary are also satisfies the given inequality.

So we will draw the solid boundary line.

The line divides the graph in to two parts one is $y<-\frac{1}{4}x+3$and other is $y>-\frac{1}{4}x+3$.

Now to draw the graph we will consider test point.

Test point: (0, 0) which is outside the boundary.

Substituting it in to the both inequality,

$0<30>3$

We know that 0 is less than 3.

Hence the test point satisfies the inequality $y<-\frac{1}{4}x+3$.

So we can draw the part of the test point side.

That is,

Hence, the graph of the two variable inequality $y≤-\frac{1}{4}x+3$is,