Question

Graph y_>1/2x-2 and y>-2x+4

Answer 1

Explanation:

The steps to graph this type of inequalities are the following:

1: Change the symbols of inequalities by symbols of equality

`y = (1)/(2)x-2` (i)

and

`y = -2x + 4` (ii)

2: Graph the equations of the line finding the cut points with the axes

(i)

`y = 0\\\\0 = (1)/(2)x -2\\\\2 =(1)/(2)x\\\\4 = x`

.......................

`x = 0\\\\y=(1)/(2)(0) -2\\\\y = -2`

-------------------------

(ii)

`y = 0\\\\0 = -2x +4\\\\-4 = -2x\\\\x = 2`

.......................

`x = 0\\\\y = -2(0) +4\\\\y = 4`

The graph of these lines is shown in the attached figure.

3: For inequality (i)

`y\geq(1)/(2)x-2` (i)

Since y is greater than or equal to
`(1)/(2)x-2` then identify the line
`y = (1)/(2)x-2` and mark the entire region above this line

For inequality (ii)

`y >-2x + 4` (ii)

Since y is greater than or equal to
`-2x + 4`, then identify the line
`y = -2x + 4` and mark the entire region above this line

At the end, the formed region comprises all the points that are above
`y = -2x + 4` and at the same time they are above
`y = 1/2x-2`

The attached graph shows this region