Question

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

Answer 1

Step-by-step explanation:

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

1: Change the symbols of inequalities by symbols of equality

$y = \frac{1}{2}x-2$ (i)

 and

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

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

(i)

$y = 0\\\\0 = \frac{1}{2}x -2\\\\2 =\frac{1}{2}x\\\\4 = x$

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

$x = 0\\\\y=\frac{1}{2}(0) -2\\\\y = -2$

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

(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)

$y\geq\frac{1}{2}x-2$ (i)

Since y is greater than or equal to $\frac{1}{2}x-2$ then identify the line $y = \frac{1}{2}x-2$ 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