# How do you graph #y+4<=1/2(x-4)#?

##### 2 Answers

See below.

#### Explanation:

Subtract 4 from both sides to get

Simplify right side to get

Because this is also an equal to inequality we can say that

This gives us the equation of a line that can be plotted.

All values that lie on the line are included values. The shaded area of included values can be found by taking a set coordinates of from either side of the line and checking them in the inequality to see if they satisfy it.

See graph:

graph{y + 4 <= (1/2)(x-4) [-25.67, 25.66, -12.83, 12.84]}

Please see below.

#### Explanation:

As

Hence first draw te graph of

When

Hence we can draw the graph of

graph{(x-2y-12)(x^2+(y+6)^2-0.02)((x-12)^2+y^2-0.02)=0 [-4.46, 15.54, -7.28, 2.72]}

This divides the Cartesian plane in three parts,

**One** - on the line - all these points satisfy the inequality

**Two** - to the left of line. Let us pick up the point

**Three** - to the right of line. Let us pick up

As the line and portion of the plane to the right of it satisfies the inequality

graph{y+4 <= 1/2(x-4) [-4.46, 15.54, -7.28, 2.72]}

Note that if we had **dotted** as shown below.

graph{y+4 < 1/2(x-4) [-4.46, 15.54, -7.28, 2.72]}